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{{Short description|British theoretical physicist (1902–1984)}}
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{{Use British English|date=January 2024}}
{{Use dmy dates|date=January 2024}}
{{Infobox scientist
| name              = Paul Dirac
| honorific_suffix  = {{Post-nominals|country=GBR|OM|FRS|size=100%}}
| image             = Paul Dirac, 1933.jpg
| caption           = Dirac in 1933
| birth_date        = {{Birth date|1902|08|08|df=yes}}
| birth_name        = Paul Adrien Maurice Dirac
| birth_place       = [[Bristol]], [[England]], [[United Kingdom of Great Britain and Ireland|UKGBI]]
| death_date        = {{Death date and age|1984|10|20|1902|08|08|df=yes}}
| death_place       = [[Tallahassee, Florida]], US
| citizenship       = {{Plain list|
* United Kingdom
* Switzerland (until 1919)
}}
| education         = {{Plain list|
* [[Bishop Road Primary School]]
* [[Cotham School|Merchant Venturers' Technical College]]
}}
| alma_mater        = {{Plain list|
* [[University of Bristol]] ([[Bachelor of Science|BSc]], [[Bachelor of Arts|BA]])
* {{No wrap|[[University of Cambridge]] ([[Doctor of Philosophy|PhD]])}}<!--St John's College doesn't award degrees-->
}}
| known_for         = {{Plain list|
* [[Fermi–Dirac statistics]] (1926)
* Work on [[quantum electrodynamics]] (1927)
* [[Dirac equation]] (1928)
* Postulating [[magnetic monopole]]s (1931)
* [[Dirac large numbers hypothesis]] (1937)
* Postulating [[gravitational wave]]s (1959)
* [[Born–Infeld model|Dirac–Born–Infeld action]] (1962)
* [[Dirac membrane]] (1962)
}}
| title             = [[Lucasian Professor of Mathematics]] (1932–69)
| spouse            = {{Marriage|Margit Wigner|1937}}
| children          = 4 in total (2 stepchildren, including [[Gabriel Andrew Dirac|Gabriel]])
| relatives         = [[Eugene Wigner]] (brother-in-law)
| awards            = {{Plain list|
* [[Fellow of the Royal Society|FRS]] (1930)
* [[Nobel Prize in Physics]] (1933)
* [[Royal Medal]] (1939)
* [[Copley Medal]] (1952)
* [[Max Planck Medal]] (1952)
* [[J. Robert Oppenheimer Memorial Prize]] (1969)
* [[Order of Merit]] (1973)
}}
| fields            = {{Plain list|
* [[Particle physics]]
* [[Quantum mechanics|Quantum physics]]
* [[Relativistic mechanics|Relativistic physics]]
}}
| work_institutions = {{Plain list|
* University of Cambridge (1927–69)
* [[Center for Theoretical Studies, University of Miami]] (1969–72)
* [[Florida State University]] <br/> (1970–84)
}}
| thesis_title      = Quantum Mechanics
| thesis_url        = https://archive.org/details/353070-dirac-paul-dissertation-secured
| thesis_year       = 1926
| doctoral_advisor  = [[Ralph Fowler]]
| doctoral_students = {{Plain list|
* [[C. J. Eliezer]] (1946)<ref name=MGP>{{Cite web|title=Paul Dirac - The Mathematics Genealogy Project|url=https://www.genealogy.math.ndsu.nodak.edu/id.php?id=18524|website=genealogy.math.ndsu.nodak.edu|access-date=2025-06-02}}</ref>
* [[Harish-Chandra]] (1947)<ref name=MGP/>
* [[Richard J. Eden]] (1951)<ref name=MGP/>
* [[Behram Kurşunoğlu]] (1952)<ref name=PhysicsTree>{{Cite web|title=Paul Adrien Maurice Dirac - Physics Tree|url=https://academictree.org/physics/peopleinfo.php?pid=48874|website=academictree.org|access-date=2025-08-05}}</ref>
* [[Dennis Sciama]] (1953)<ref name=MGP/>
* [[John Polkinghorne]] (1955)
<!-- Not in article
* [[Behram Kurşunoğlu]]<ref>[[Cécile DeWitt-Morette|DeWitt, C. M.]], & Rickles, D., eds., ''The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference'' (Berlin: Edition Open Access, 2011), p. 30.</ref>
-->
}}
| notable_students  = {{Plain list|
* [[Homi J. Bhabha]]
* [[Freeman Dyson]]
* [[Fred Hoyle]]
* [[Herbert Jehle]]<ref name=PhysicsTree/>
* [[Victor Weisskopf]]
}}
}}

'''Paul Adrien Maurice Dirac''' ({{IPAc-en|d|ɪ|ˈ|r|æ|k}} {{Respell|dih|RAK}};<ref>{{Cite web|title=DIRAC Definition & Meaning|url=https://www.dictionary.com/browse/dirac|website=[[dictionary.com]]|access-date=2025-06-02}}</ref> 8 August 1902 – 20 October 1984) was a British [[theoretical physicist]] who is considered to be one of the founders of [[quantum mechanics]].<ref>{{cite book |last=Simmons |first=John |url=https://archive.org/details/100mostinfluenti0000simm/page/104 |title=The Scientific 100: A Ranking of the Most Influential Scientists, Past and Present |publisher=Carol Publishing Group |year=1997 |isbn=978-0-8065-1749-0 |location=[[Secaucus, New Jersey]] |pages=104–108 |language=en}}</ref><ref>[[Narasimhaiengar Mukunda|Mukunda, N.]], ''Images of Twentieth Century Physics'' ([[Bangalore]]: [[Jawaharlal Nehru Centre for Advanced Scientific Research]], 2000), [https://books.google.com/books?id=YFGJ2PAEUmwC&pg=PP9 p. 9].</ref> Dirac laid the foundations for both [[quantum electrodynamics]] and [[quantum field theory]].<ref name="Berry-1998" /><ref name="Duck-1998">{{Cite book |last1=Duck |first1=Ian |url=https://archive.org/details/paulispinstatist0000unse/page/149 |title=Pauli and the Spin-Statistics Theorem |last2=Sudarshan |first2=E. C. G. |author-link2=E. C. G. Sudarshan |publisher=World Scientific Publishing |year=1998 |isbn=978-981-02-3114-9 |pages=149–167 |language=en |chapter=Chapter 6: Dirac's Invention of Quantum Field Theory}}</ref><ref name="plato.stanford.edu" /><ref name="Bhaumik-2022">{{Cite journal |last=Bhaumik |first=Mani L. |date=2022 |title=How Dirac's Seminal Contributions Pave the Way for Comprehending Nature's Deeper Designs |journal=Quanta |volume=8 |issue=1 |pages=88–100 |doi=10.12743/quanta.v8i1.96 |arxiv=2209.03937 |s2cid=212835814 }}</ref> He was the [[Lucasian Professor of Mathematics]] at the [[University of Cambridge]] from 1932 to 1969 and a professor of physics at [[Florida State University]] from 1970 to 1984. Dirac shared the 1933 [[Nobel Prize in Physics]] with [[Erwin Schrödinger]] "for the discovery of new productive forms of [[atomic theory]]".<ref name="nobel">{{cite web |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1933/ |title=The Nobel Prize in Physics 1933 |publisher=The Nobel Foundation |access-date=4 April 2013}}</ref>

Dirac graduated from the [[University of Bristol]] with a [[first class honours]] Bachelor of Science degree in electrical engineering in 1921, and a first class honours Bachelor of Arts degree in mathematics in 1923.<ref>{{Cite book |last=Schmitz |first=Kenneth S. |url=https://books.google.com/books?id=4WGdBgAAQBAJ&pg=PA310 |title=Physical Chemistry: Multidisciplinary Applications in Society |publisher=Elsevier |year=2018 |isbn=978-0-12-800513-2 |page=310}}</ref> Dirac then graduated from [[St John's College, Cambridge]] with a PhD in physics in 1926, writing the first ever thesis on quantum mechanics.<ref>{{Cite web |last=Gordin |first=Michael D. |date=6 February 2017 |title=Dr. Strange |url=https://www.americanscientist.org/article/dr-strange |access-date=29 May 2024 |website=American Scientist}}</ref>

Dirac made fundamental contributions to the early development of both quantum mechanics and [[quantum electrodynamics]], coining the latter term.<ref name="plato.stanford.edu">{{Cite web |title=Quantum Field Theory > The History of QFT (Stanford Encyclopedia of Philosophy) |url=https://plato.stanford.edu/entries/quantum-field-theory/qft-history.html |access-date=22 October 2023 |website=plato.stanford.edu}}</ref> Among other discoveries, he formulated the [[Dirac equation]] in 1928. It connected [[special relativity]] and quantum mechanics and predicted the existence of [[antimatter]].<ref name=NYTObit>{{cite news| title=PAUL DIRAC, NOBEL LAUREATE; DEVELOPED MODEL OF THE ATOM| date=October 22, 1984| work=[[The New York Times]]| url=https://www.nytimes.com/1984/10/22/obituaries/paul-dirac-nobel-laureate-developed-theory-of-atom.html}}</ref><ref name="timeline.web.cern.ch">{{Cite web |title=Discovering the positron |url=https://timeline.web.cern.ch/timeline-header/142#416 |access-date=23 October 2023 |website=timeline.web.cern.ch}}</ref> The Dirac equation is one of the most important results in physics,<ref name="Berry-1998">{{Cite web |last=Berry |first=Michael |author-link=Michael Berry (physicist) |date=1 February 1998 |title=Paul Dirac: the purest soul in physics |url=https://physicsworld.com/paul-dirac-the-purest-soul-in-physics/ |access-date=16 October 2023 |website=[[Physics World]] |language=en-GB}}</ref> regarded by some physicists as the "real seed of modern physics".<ref name="Zichichi-2000">{{Cite web |last=Zichichi |first=Antonino |author-link=Antonino Zichichi |date=2 March 2000 |title=Dirac, Einstein and physics |url=https://physicsworld.com/a/dirac-einstein-and-physics/ |access-date=22 October 2023 |website=[[Physics World]] |language=en-GB}}</ref> He wrote a famous paper in 1931,<ref>{{Cite journal |last=Dirac |first=Paul |date=1931 |title=Quantised singularities in the electromagnetic field |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=133 |issue=821 |pages=60–72 |doi=10.1098/rspa.1931.0130 |bibcode=1931RSPSA.133...60D |issn=0950-1207|doi-access=free }}</ref> which further predicted the existence of antimatter.<ref name="Gottfried-2011">{{Cite journal |last=Gottfried |first=Kurt |date=2011 |title=P. A. M. Dirac and the discovery of quantum mechanics |url=https://pubs.aip.org/aapt/ajp/article-abstract/79/3/261/398648/P-A-M-Dirac-and-the-discovery-of-quantum-mechanics?redirectedFrom=fulltext |journal=American Journal of Physics |volume=79 |issue=3 |pages=2, 10|doi=10.1119/1.3536639 |arxiv=1006.4610 |bibcode=2011AmJPh..79..261G |s2cid=18229595 }}</ref><ref>{{Citation |last=Kragh |first=Helge |title=Paul Dirac and The Principles of Quantum Mechanics |date=10 September 2013 |url=https://mprl-series.mpg.de/studies/2/11/index.html |work=Research and Pedagogy: A History of Quantum Physics through Its Textbooks |access-date=23 October 2023 |series=MPRL – Studies |place=Berlin |publisher=Max-Planck-Gesellschaft zur Förderung der Wissenschaften |language=english |isbn=978-3-945561-24-9 |author-link=Helge Kragh}}</ref><ref name="timeline.web.cern.ch" /> Dirac also contributed greatly to the reconciliation of [[general relativity]] with quantum mechanics. He contributed to [[Fermi–Dirac statistics]], which describes the behaviour of [[fermion]]s, particles with half-integer [[Spin (physics)|spin]]. His 1930 monograph, [[The Principles of Quantum Mechanics|''The'' ''Principles of Quantum Mechanics'']], is one of the most influential texts on the subject.<ref>{{Cite journal |last=Brown |first=Laurie M. |author-link=Laurie Brown (physicist) |date=2006 |title=Paul A. M. Dirac's Principles of Quantum Mechanics |url=https://faculty.washington.edu/seattle/physics441/online/about%20Dirac.pdf |journal=Physics in Perspective |volume=8|issue=4 |pages=381–407 |doi=10.1007/s00016-006-0276-4 |bibcode=2006PhP.....8..381B |s2cid=120303937 }}</ref>

In 1987, [[Abdus Salam]] declared that "Dirac was undoubtedly one of the greatest physicists of this or any century ... No man except [[Albert Einstein|Einstein]] has had such a decisive influence, in so short a time, on the course of physics in this century."<ref>{{Cite book |last1=Kursunoglu |first1=Behram N. |url=https://archive.org/details/pauladrienmauric0000unse/page/262 |title=Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist |last2=Wigner |first2=Eugene P. |publisher=Cambridge University Press |year=1987 |isbn=978-0-521-34013-7 |pages=262 |language=en}}</ref> In 1995, [[Stephen Hawking]] stated that "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe".<ref>{{Cite web |date=25 August 2009 |title=The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius |url=https://cerncourier.com/a/the-strangest-man-the-hidden-life-of-paul-dirac-quantum-genius/ |access-date=22 October 2023 |website=CERN Courier |language=en-GB}}</ref> [[Antonino Zichichi]] asserted that Dirac had a greater impact on modern physics than Einstein,<ref name="Zichichi-2000" /> while [[Stanley Deser]] remarked that "We all stand on Dirac's shoulders."<ref>{{Cite journal |last=Deser |first=Stanley |author-link=Stanley Deser |date=2004 |title=P.A.M. Dirac and the Development of Modern General Relativity |url=https://www.worldscientific.com/doi/abs/10.1142/S0217751X04018622 |journal=International Journal of Modern Physics A |language=en |volume=19 |issue=supp01 |pages=99–105 |doi=10.1142/S0217751X04018622 |bibcode=2004IJMPA..19S..99D |issn=0217-751X|url-access=subscription }}</ref>

==Early life==
Paul Adrien Maurice Dirac was born on 8 August 1902 at his parents' home in [[Bristol]], England,<ref>{{harvnb|Farmelo|2009|p=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA10 10]}}</ref> and grew up in the [[Bishopston, Bristol|Bishopston]] area of the city.<ref>{{harvnb|Farmelo|2009|pp=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA18 18–19]}}</ref> His father, Charles Adrien Ladislas Dirac, was an immigrant from [[Saint-Maurice, Switzerland]], of [[French people|French]] descent,<ref name="frs">{{Cite journal | last1 = Dalitz | first1 = R. H. | author-link1 = Richard Dalitz| last2 = Peierls | first2 = R. | author-link2 = Rudolf Peierls| doi = 10.1098/rsbm.1986.0006 | title = Paul Adrien Maurice Dirac. 8 August 1902 – 20 October 1984 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 32 | pages = 137–185 | year = 1986 | jstor = 770111| doi-access = free }}</ref> who worked in Bristol as a French teacher. His mother, Florence Hannah Dirac, née Holten, was born to a [[Cornish people|Cornish]] [[Methodism|Methodist]] family in [[Liskeard]], [[Cornwall]].<ref name="Cern Courier-2002">{{cite web|title=Paul Dirac: a genius in the history of physics|url=http://cerncourier.com/cws/article/cern/28693|work=Cern Courier|access-date=4 February 2022|date=15 August 2002|archive-date=5 October 2013|archive-url=https://web.archive.org/web/20131005014459/http://cerncourier.com/cws/article/cern/28693}}</ref><ref>{{harvnb|Farmelo|2009|pp=8, 441}}</ref> She was named after [[Florence Nightingale]] by her father, a ship's captain, who had met Nightingale while he was a soldier during the [[Crimean War]].<ref>{{harvnb|Farmelo|2009|pp=8}}</ref> His mother moved to Bristol as a young woman, where she worked as a librarian at the [[Bristol Central Library]]; despite this she still considered her identity to be Cornish rather than English.<ref>{{harvnb|Farmelo|2009|pp=441}}</ref> Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix,<ref>{{harvnb|Kragh|1990|p=1}}</ref><ref>{{harvnb|Farmelo|2009|pp=10–11}}</ref> who died by suicide in March 1925.<ref>{{harvnb|Farmelo|2009|pp=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA77 77–78]}}</ref> Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much ... I never knew that parents were supposed to care for their children, but from then on I knew."<ref>{{harvnb|Farmelo|2009|p=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA79 79]}}</ref>

Charles and the children were officially Swiss nationals until they became [[naturalised]] on 22 October 1919.<ref>{{harvnb|Farmelo|2009|p=34}}</ref> Dirac's father was strict and authoritarian, although he disapproved of corporal punishment.<ref>{{harvnb|Farmelo|2009|p=22}}</ref> Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French so that they might learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.<ref>{{harvnb|Mehra|1972|p=17}}</ref><ref>{{harvnb|Kragh|1990|p=2}}</ref>

==Education==
Dirac was educated first at [[Bishop Road Primary School]]<ref>{{harvnb|Farmelo|2009|pp=13–17}}</ref> and then at the all-boys [[Society of Merchant Venturers|Merchant Venturers']] Technical College (later [[Cotham School]]), where his father was a French teacher.<ref>{{harvnb|Farmelo|2009|pp=20–21}}</ref> The school was an institution attached to the [[University of Bristol]], which shared grounds and staff.<ref name="Mehra18"/> It emphasised technical subjects like bricklaying, shoemaking and metalwork, and modern languages.<ref>{{harvnb|Farmelo|2009|p=23}}</ref> This was unusual at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express his gratitude.<ref name="Mehra18">{{harvnb|Mehra|1972|p=18}}</ref> One of his peers at Bishop Road School was Archibald Leach, later famous as [[Cary Grant]].{{sfnp| Farmelo| 2009| p=14}}

Dirac studied [[electrical engineering]] on a City of Bristol University Scholarship at the University of Bristol's engineering faculty, which was co-located with the Merchant Venturers' Technical College.<ref>{{harvnb|Farmelo|2009|p=28}}</ref> Shortly before he completed his degree in 1921, he sat for the entrance examination for [[St John's College, Cambridge]]. He passed and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge. Despite having graduated with a [[first class honours]] [[B.Sc.]] in electrical engineering, the economic climate of the [[Post–World War I recession|post-war depression]] was such that he was unable to find work as an engineer. Instead, he took up an offer to study for a [[B.A.]] in mathematics at the University of Bristol free of charge. He was permitted to skip the first year of the course owing to his engineering degree.<ref>{{harvnb|Farmelo|2009|pp=46–47}}</ref> Under the influence of Peter Fraser, whom Dirac called the best mathematics teacher, he had the most interest in [[projective geometry]], and began applying it to the geometrical version of relativity [[Hermann Minkowski]] developed.<ref>{{Cite journal |last=Galison |first=Peter |date=2000 |title=The Suppressed Drawing: Paul Dirac's Hidden Geometry |journal=Representations |issue=72 |pages=145–166 |doi=10.2307/2902912 |jstor=2902912 |issn=0734-6018}}</ref>

In 1923, Dirac graduated, once again with first class honours, and received a £140 scholarship from the [[Department of Scientific and Industrial Research (United Kingdom)|Department of Scientific and Industrial Research]].<ref>{{harvnb|Farmelo|2009|p=53}}</ref> Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of [[general relativity]], an interest he had gained earlier as a student in Bristol, and in the nascent field of [[quantum physics]], under the supervision of [[Ralph Fowler]].<ref>{{harvnb|Farmelo|2009|pp=52–53}}</ref> From 1925 to 1928, he held an [[1851 Research Fellowship]] from the [[Royal Commission for the Exhibition of 1851]].<ref name="1851 Royal Commission Archives">1851 Royal Commission Archives</ref> He completed his [[Ph.D.]] in June 1926 with the first thesis on [[quantum mechanics]] to be submitted anywhere.<ref>{{harvnb|Farmelo|2009|p=101}}</ref> He then continued his research in [[Copenhagen]] and [[Göttingen]].<ref name="1851 Royal Commission Archives"/> In the spring of 1929, he was a visiting professor at the [[University of Wisconsin–Madison]].<ref>{{cite book |editor1-last=Kursunoglu |editor1-first=Behram N. |editor2-last=Wigner |editor2-first=Eugene Paul |title=Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist |date=1990 |publisher=Cambridge University Press |isbn=0-521-38688-8 |page=132 |url=https://books.google.com/books?id=1Pg7t9a_AX4C&q=paul+dirac+university+of+wisconsin+1929&pg=PA132 |access-date=30 September 2020}}</ref><ref>{{cite web |title=Paul Adrien Maurice Dirac |url=https://pages.hep.wisc.edu/~ldurand/715html/courseinfo/biographies/dirac.html |publisher=University of Wisconsin-Madison |access-date=30 September 2020}}</ref>

==Personal life==
===Family===
[[File:Dirac,Paul 1963 Kopenhagen.jpg|thumb|Paul and Manci Dirac in [[Copenhagen]], July 1963]]

In 1937, Dirac married<ref>{{harvnb|Farmelo|2009|p=284}}</ref> Margit Wigner, the sister of physicist [[Eugene Wigner]]<ref>{{harvnb|Farmelo|2009|p=253}}</ref> and a divorcee.<ref>{{harvnb|Farmelo|2009|p=256}}</ref> Dirac raised Margit's two children, Judith and [[Gabriel Andrew Dirac|Gabriel]], as if they were his own.<ref>{{harvnb|Farmelo|2009|p=288}}</ref> Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.<ref>{{harvnb|Farmelo|2009|pp=305, 323}}</ref>

Margit, known as Manci, had visited her brother in 1934 in [[Princeton, New Jersey]], from their native Hungary and, while at dinner at the Annex Restaurant, met the "lonely-looking man at the next table". This account from a Korean physicist, [[Young Suh Kim|Y. S. Kim]], who met and was influenced by Dirac, also says: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46. Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else".<ref>{{cite web |url=http://ysfine.com/dirac/wigsis.html |title=Wigner's Sisters |last=Kim |first=Young Suh |year=1995 |archive-url= https://web.archive.org/web/20080303112257/https://ysfine.com/dirac/wigsis.html |archive-date= 3 March 2008}}</ref>

===Personality===
[[File:Clara Ewald - Paul Dirac.jpg|thumb|upright|Portrait of Paul Dirac by [[Clara Ewald]], 1939]]
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to [[Paul Ehrenfest]], [[Albert Einstein]] wrote of a Dirac paper, "I am toiling over Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter concerning the [[Compton scattering|Compton effect]] he wrote, "I don't understand the details of Dirac at all."<ref>{{harvnb|Kragh|1990|p=82]}}  "Dirac verstehe ich im Einzelnen überhaupt nicht (Compton-Effekt)"</ref>
Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit called a "dirac", which was one word per hour.<ref>{{harvnb|Farmelo|2009|p=89}}</ref> When [[Niels Bohr]] complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it."<ref name="standy">{{cite web |url=https://web.archive.org/web/20251102192101/https://mathshistory.st-andrews.ac.uk/Biographies/Dirac/|title=Paul Adrien Maurice Dirac |publisher=University of St. Andrews |access-date=2 November 2025}}</ref> He criticised the physicist [[J. Robert Oppenheimer]]'s interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible."<ref>{{harvnb|Mehra|1972|pp=[https://books.google.com/books?id=CpJiqUFkHGoC&pg=PA17 17–59]}}</ref> Bohr called Dirac "a complete logical genius" and also the "strangest man" who had ever visited his Institute.{{sfnp| Farmelo| 2009| p=120}}

Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and stopped only on Sunday when he took long strolls alone.<ref>{{harvnb|Kragh|1990|p=17}}</ref>

An anecdote recounted in a review of the 2009 biography tells of [[Werner Heisenberg]] and Dirac sailing on an ocean liner to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac—'an Edwardian geek', as biographer [[Graham Farmelo]] puts it—suffered agonies if forced into any kind of socializing or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice?{{' "}}<ref name="mckie">{{cite web |url=https://www.theguardian.com/books/2009/feb/01/strangest-man-paul-dirac-review |title=Anti-matter and madness |last1=McKie |first1=Rob |date=1 February 2009 |work=The Guardian |access-date=4 April 2013}}</ref>

Margit Dirac told both [[George Gamow]] and Anton Capri in the 1960s that her husband had said to a house visitor, "Allow me to present Wigner's sister, who is now my wife."<ref>{{harvnb|Gamow|1966|p=121}}</ref><ref>{{harvnb|Capri|2007|p=148}}</ref>

[[File:Paul Dirac and Richard Feynman at Jabłonna 1962.png|thumb|Paul Dirac and Richard Feynman at Jabłonna, Poland. July 1962.]]
Another story told of Dirac is that when he first met the young [[Richard Feynman]] at a conference, he said after a long silence, "I have an equation. Do you have one too?"<ref>{{harvnb|Zee|2010|p=105}}</ref>

After he presented a lecture at a conference, one colleague raised his hand and said: "I don't understand the equation on the top-right-hand corner of the blackboard". After a long silence, the moderator asked Dirac if he wanted to answer the question, to which Dirac replied: "That was not a question, it was a comment."<ref>{{cite news | url=https://www.theglobeandmail.com/arts/books-and-media/review-the-strangest-man-by-graham-farmelo/article4289494/ | title=A quantum leap into oddness | first=Chet | last=Raymo | newspaper=[[The Globe and Mail]] | date=17 October 2009}} (Review of Farmelo's ''The Strangest Man''.)</ref><ref>{{harvnb|Farmelo|2009|pp=161–162}}, who attributes the story to [[Niels Bohr]].</ref>

Dirac was also noted for his personal modesty. He called the equation for the [[time evolution]] of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of [[Fermi–Dirac statistics]] for half-integer-spin particles ([[fermions]]) and [[Bose–Einstein statistics]] for integer-spin particles ([[bosons]]). While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Bose statistics" for reasons, he explained, of "symmetry".<ref>{{cite book|last1=Mehra|first1=Jagdish|last2=Rechenberg|first2=Helmut|author-link1=Jagdish Mehra |author-link2=Helmut Rechenberg |title=The Historical Development of Quantum Theory|year=2001|publisher=Springer Science & Business Media|isbn=978-0-387-95180-5|page=746|url=https://books.google.com/books?id=-pL56OcVubgC&q=Paul+Dirac+Einstein+statistics+Symmetry&pg=PA746}}</ref>

===Philosophy of physics ===
When asked to summarize his philosophy of physics, Dirac wrote "Physical laws should have mathematical beauty."{{sfnp| Farmelo| 2009| p=359}}

Dirac was famously not bothered by [[Interpretations of quantum mechanics|issues of interpretation in quantum theory]]. In fact, in a paper published in a book in his honour, he wrote: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here.  I want to deal with more fundamental things."<ref>Dirac, "The inadequacies of quantum field theory", in B. N. Kursunoglu & E. P. Wigner, eds., [https://books.google.com/books?id=1Pg7t9a_AX4C ''Paul Adrien Maurice Dirac''] (Cambridge: Cambridge University Press, 1987), p. 194.</ref>

===Views on religion===
Werner Heisenberg recollected a conversation among young participants at the 1927 [[Solvay Conference]] about Einstein and [[Max Planck]]'s views on religion between [[Wolfgang Pauli]], Heisenberg and Dirac. Dirac's contribution was a criticism of the political purpose of religion, which Bohr regarded as quite lucid when hearing it from Heisenberg later.<ref>[[Abraham Pais|Pais, A.]], ''Niels Bohr's Times: In Physics, Philosophy, and Polity'' (Oxford: [[Oxford University Press#Clarendon Press|Clarendon Press]], 1991), [https://archive.org/details/nielsbohrstimesi0000pais/page/320 p. 320].</ref> Heisenberg's view was tolerant. Pauli, raised as a Catholic, had kept silent after some initial remarks, but when finally he was asked for his opinion, said: "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God, and Paul Dirac is His prophet.{{' "}} Everybody, including Dirac, burst into laughter.<ref>{{harvnb|Heisenberg|1971|p=87}}</ref><ref>{{harvnb|Farmelo|2009|p=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA138 138]}}, who says this was an old joke, pointing out a [[Punch (magazine)|''Punch'']] footnote in the 1850s that "There is no God, and [[Harriet Martineau]] is her prophet."</ref>

Later in life, in an article mentioning God that appeared in the May 1963 edition of ''[[Scientific American]]'', Dirac wrote:
<blockquote>It seems to be one of the fundamental features of nature that fundamental [[physical law]]s are described in terms of a [[mathematical theory of great beauty]] and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.<ref>{{cite web |url=http://blogs.scientificamerican.com/guest-blog/2010/06/25/the-evolution-of-the-physicists-picture-of-nature/ |title=The Evolution of the Physicist's Picture of Nature |last1=Dirac |first1=Paul |date=May 1963 |work=[[Scientific American]] |access-date=4 April 2013}}</ref></blockquote>

In 1971, at a conference meeting, Dirac described the possibilities for scientifically answering the question of God.
<ref>{{harvnb|Kragh|1990|pp=256–257}}</ref> Dirac explained that 
<blockquote>... if physical laws are such that to start off life involves an excessively small chance so that it will not be reasonable to suppose that life would have started just by blind chance, then there must be a god,... On the other hand, if life can start very easily and does not need any divine influence, then I will say that there is no god.<ref name="Kragh 1990">{{harvnb|Kragh|1990}}</ref></blockquote>

==Research==
[[File:Solvay conference 1927.jpg|thumb|The 1927 [[Solvay Conference]] in Brussels, a gathering of the world's top physicists. Dirac is in the centre of the middle row, seated behind [[Albert Einstein]].]]
[[File:DIAS_1942_photo.jpg|thumb|Dirac (front row 3rd from left), next to [[Éamon de Valera]] (front row 4th from left), [[Erwin Schrödinger]] (front row 2nd from right) at [[Dublin Institute for Advanced Studies]] in 1942]]
Dirac discovered the [[Dirac equation|relativistic equation for the electron]], which now bears his name. The remarkable notion of an antiparticle to each fermion particle – e.g. the positron as antiparticle to the electron – stems from his equation. He is credited as being the one to create [[quantum field theory]], which underlies all theoretical work on sub-atomic or "elementary" particles today, work that is fundamental to our understanding of the forces of nature, alongside creating quantum electrodynamics and coining the term.<ref name="Duck-1998" /><ref name="Bhaumik-2022" /> He proposed and investigated the concept of a [[magnetic monopole]], an object not yet known empirically, as a means of bringing even greater symmetry to [[James Clerk Maxwell]]'s equations of [[electromagnetism]]. Dirac also coined the terms "[[fermion]]" (particles with half-integer spin) and "[[boson]]" (particles with whole-integer spin).<ref>{{harvnb|Farmelo|2009|pp=331}}</ref>

Throughout his career, Dirac was motivated by the principles of [[mathematical beauty]],<ref name="Diracmathshistory">{{Cite web |title=Paul Dirac - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Dirac/ |access-date=31 December 2023 |website=Maths History |language=en}}</ref> with [[Peter Goddard (physicist)|Peter Goddard]] stating that "Dirac cited mathematical beauty as the ultimate criterion for selecting the way forward in theoretical physics".<ref>{{Cite book |last=Goddard |first=Peter |url=https://archive.org/details/isbn_0521583829 |title=Paul Dirac: The Man and his Work |publisher=Cambridge University Press |year=1998 |isbn=978-0-521-58382-4 |pages=x |language=en}}</ref> Dirac was recognised for being mathematically gifted, as during his time in university, academics had affirmed that Dirac had an "ability of the highest order in mathematical physics",<ref>{{harvnb|Farmelo|2009|pp=82}}</ref> with [[Ebenezer Cunningham]] stating that Dirac was "quite the most original student I have met in the subject of mathematical physics".<ref>{{harvnb|Farmelo|2009|pp=76}}</ref> Therefore, Dirac was known for his "astounding physical intuition combined with the ability to invent new mathematics to create new physics".<ref name="Gottfried-2011" /> During his career, Dirac made numerous important contributions to mathematical subjects, including the [[Dirac delta function]], [[Dirac algebra]] and the [[Dirac operator]].

===Quantum theory===
Dirac's first step into a new quantum theory was taken late in September 1925. [[Ralph Fowler]], his research supervisor, had received a proof copy of an [[Über quantentheoretischer Umdeutung|exploratory paper]] by [[Werner Heisenberg]] in the framework of the old quantum theory of Bohr and [[Arnold Sommerfeld|Sommerfeld]]. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the [[matrix mechanics|matrix formulation]] of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.<ref name="Farmelo 2009 83–88">{{harvnb|Farmelo|2009|pp=83–88}}</ref>

Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had established. Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the [[Poisson bracket]]s that occur in the [[classical mechanics|classical dynamics]] of particle motion.<ref name="Farmelo 2009 83–88"/> At the time, his memory of Poisson brackets was rather vague, but he found [[E. T. Whittaker]]'s ''[[Analytical Dynamics of Particles and Rigid Bodies]]'' illuminating.<ref name="Coutinho12">{{Cite journal|last=Coutinho|first=S. C.|date=1 May 2014|title=Whittaker's analytical dynamics: a biography|journal=Archive for History of Exact Sciences|language=en|volume=68|issue=3|pages=355–407|doi=10.1007/s00407-013-0133-1|issn=1432-0657|s2cid=122266762}}</ref> From his new understanding, he developed a quantum theory based on [[Commutative property|non-commuting]] dynamical variables. This led him to the most profound and significant general formulation of quantum mechanics to date.<ref>{{cite news|title=Paul Dirac: a genius in the history of physics|url=http://cerncourier.com/cws/article/cern/28693|work=Cern Courier|access-date=13 May 2013|date=15 August 2002|archive-date=5 October 2013|archive-url=https://web.archive.org/web/20131005014459/http://cerncourier.com/cws/article/cern/28693}}</ref> His novel formulation using [[Dirac bracket]]s allowed him to obtain the [[quantization (physics)|quantisation]] rules in a [[Canonical quantization|novel and more illuminating manner]]. For this work,<ref name="Dirac1926">{{cite journal| title=On the Theory of Quantum Mechanics| journal=Proceedings of the Royal Society A| year=1926| first=Paul A. M.| last=Dirac| author-link=Paul Dirac| volume=112| issue=762| pages=661–77| jstor=94692| doi=10.1098/rspa.1926.0133 |bibcode = 1926RSPSA.112..661D | doi-access=free}}</ref> published in 1926, Dirac received a PhD from Cambridge.

===Fermi–Dirac statistics===
{{Main|Fermi–Dirac statistics}}
Shortly after [[Wolfgang Pauli]] proposed his [[Pauli exclusion principle]] (that two electrons cannot occupy the same quantum energy level), [[Enrico Fermi]] and Dirac<ref name="Dirac1926"/> both realized the principle would dramatically alter the statistical mechanics of electron systems. This work became the basis for [[Fermi–Dirac statistics]].<ref>{{Cite journal |last=Domb |first=Cyril |date=2003 |title=Some Observations on the Early History of Equilibrium Statistical Mechanics |url=http://link.springer.com/10.1023/A:1022139230789 |journal=Journal of Statistical Physics |volume=110 |issue=3/6 |pages=475–496 |doi=10.1023/A:1022139230789|bibcode=2003JSP...110..475D |url-access=subscription }}</ref>{{rp|488}} This applies to systems consisting of many identical [[spin-1/2]] particles, or [[fermions]] (i.e. that obey the Pauli exclusion principle), e.g. electrons in solids and liquids, and importantly to the field of conduction in [[semiconductor]]s.

===Dirac equation===
{{Main|Dirac equation}}
In 1928, building on 2×2 spin matrices which he purported to have discovered independently of [[Wolfgang Pauli]]'s work on non-relativistic [[Spin (physics)|spin]] systems (Dirac told [[Abraham Pais]], "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."),<ref>{{cite book|title=Reminiscences about a Great Physicist|publisher=Cambridge University Press|page=[https://books.google.com/books?id=1Pg7t9a_AX4C&pg=PA98 98]|editor1=Behram N. Kurşunoğlu |editor2=Eugene Paul Wigner }}</ref> he proposed the [[Dirac equation]] as a [[Special relativity|relativistic]] [[equation of motion]] for the [[wave function]] of the [[electron]].<ref>{{cite journal |last=Dirac |first=P. A. M. |title=The Quantum Theory of the Electron  |journal=Proceedings of the Royal Society of London A |date=1 February 1928 |volume=117 |issue=778 |pages=610–24 |doi=10.1098/rspa.1928.0023 |bibcode=1928RSPSA.117..610D|doi-access=free }}</ref> This work led Dirac to predict the existence of the [[positron]], the electron's [[antiparticle]], which he interpreted in terms of what came to be called the ''[[Dirac sea]]''.<ref>{{Nobelprize}} with his Nobel Lecture, 12 December 1933 ''Theory of Electrons and Positrons''</ref> The positron was observed by [[Carl David Anderson|Carl Anderson]] in 1932. Dirac's equation also contributed to explaining the origin of [[Spin (physics)|quantum spin]] as a relativistic phenomenon.

The necessity of [[fermion]]s (matter) being created and destroyed in [[Enrico Fermi]]'s 1934 theory of [[beta decay]] led to a reinterpretation of Dirac's equation as a "classical" [[field equation]] for any [[point particle]] of spin ''[[Planck constant|ħ]]''/2, itself subject to quantisation conditions involving [[Anticommutativity|anti-commutators]]. Thus reinterpreted, in 1934 by [[Werner Heisenberg]], as a (quantum) field equation accurately describing all elementary matter particles – today [[quark]]s and [[lepton]]s – this [[Dirac field]] equation is as central to theoretical physics as the [[Maxwell equations|Maxwell]], [[Yang–Mills theory|Yang–Mills]] and [[General relativity|Einstein]] field equations. Dirac is regarded as the founder of [[quantum electrodynamics]], being the first to use that term. He also introduced the idea of [[vacuum polarisation]] in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, in particular [[Julian Schwinger]], [[Richard Feynman]], [[Sin-Itiro Tomonaga]] and [[Freeman Dyson]] in their formulation of quantum electrodynamics.

Dirac's [[The Principles of Quantum Mechanics|''The'' ''Principles of Quantum Mechanics'']], published in 1930, is a landmark in the [[history of science]]. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Heisenberg on [[matrix mechanics]] and of [[Erwin Schrödinger]] on [[Schrödinger equation|wave mechanics]] into a single mathematical formalism that associates measurable quantities to operators acting on the [[Hilbert space]] of vectors that describe the state of a [[physical system]]. The book also introduced the [[Dirac delta function]]. Following his 1939 article,<ref>{{cite journal|author=P. A. M. Dirac |year=1939 |title=A New Notation for Quantum Mechanics |journal=Proceedings of the Cambridge Philosophical Society |volume=35 |issue=3 |page=416 |doi=10.1017/S0305004100021162 |bibcode=1939PCPS...35..416D|s2cid=121466183 }}</ref> he also included the [[bra–ket notation]] in the third edition of his book,<ref>{{cite journal |author1=Gieres |doi=10.1088/0034-4885/63/12/201 |title=Mathematical surprises and Dirac's formalism in quantum mechanics |year=2000 |volume=63 |issue=12 |page=1893 |journal=Reports on Progress in Physics |arxiv=quant-ph/9907069 |bibcode = 2000RPPh...63.1893G|s2cid=10854218 }}</ref> thereby contributing to its universal use nowadays.

===Quantum electrodynamics===
Dirac's [[quantum electrodynamics]] (QED) included terms with infinite [[self-energy]]. A workaround known as [[renormalisation]] was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation", he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!"<ref>{{harvnb|Kragh|1990|p=184}}</ref> His refusal to accept renormalisation resulted in his work on the subject moving increasingly out of the mainstream. [[Shin'ichirō Tomonaga]], [[Julian Schwinger|Schwinger]] and [[Richard Feynman|Feynman]] mastered this approach, producing a QED with unprecedented accuracy, resulting in formal recognition by being awarded the 1965 Nobel Prize in Physics.<ref>{{harvnb|Schweber|1994}}</ref>

In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints<ref>{{Cite journal |last=Dirac |first=P. a. M. |date=1950 |title=Generalized Hamiltonian Dynamics |url=https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/generalized-hamiltonian-dynamics/F4C30A59B59BEE09E9CB6F07377B8BD3 |journal=Canadian Journal of Mathematics |language=en |volume=2 |pages=129–148 |doi=10.4153/CJM-1950-012-1 |issn=0008-414X}}</ref><ref>{{Cite journal |last=Dirac |first=P. a. M. |date=1951 |title=The Hamiltonian Form of Field Dynamics |url=https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/hamiltonian-form-of-field-dynamics/E17F213F85E3377BC2EBB3A1E0876BC8 |journal=Canadian Journal of Mathematics |language=en |volume=3 |pages=1–23 |doi=10.4153/CJM-1951-001-2 |issn=0008-414X}}</ref> based{{citation needed|date=July 2024}} on lectures that he delivered at the 1949 [[International Congress of Mathematicians|International Mathematical Congress]] in Canada. Dirac had also solved the problem of putting the [[Schwinger–Tomonaga equation]] into the Schrödinger representation<ref>Phillips R. J. N. 1987 ''Tributes to Dirac'' p31 London: Adam Hilger</ref> and given explicit expressions for the [[Scalar field|scalar meson field]] ([[pion|spin zero pion]] or [[pseudoscalar meson]]), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon).

===Magnetic monopoles===
In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge.<ref>
{{cite journal
 |author = Dirac, P. A. M.
 |journal = [[Proceedings of the Royal Society#Proceedings of the Royal Society A|Proceedings of the Royal Society A]]
 |doi = 10.1098/rspa.1931.0130
 |pages = 60–72
 |title = Quantised Singularities in the Electromagnetic Field
 |volume = 133
 |issue = 821
 |year = 1931
 |bibcode = 1931RSPSA.133...60D
	|doi-access = free
 }}</ref> 
No such monopole has been detected, despite numerous attempts and preliminary claims.<ref>{{Cite journal |last1=Patrizii |first1=L. |last2=Spurio |first2=M. |date=2015-10-19 |title=Status of Searches for Magnetic Monopoles |url=https://www.annualreviews.org/doi/10.1146/annurev-nucl-102014-022137 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=65 |issue=1 |pages=279–302 |doi=10.1146/annurev-nucl-102014-022137 |issn=0163-8998|arxiv=1510.07125 |bibcode=2015ARNPS..65..279P }}</ref> (See also: [[Magnetic monopole#Searches for magnetic monopoles|Searches for magnetic monopoles]].)

===War work===
Dirac contributed to the [[Tube Alloys]] project, the British programme to research and construct atomic bombs during [[World War II]].<ref>{{Cite ODNB|last=Cathcart|first=Brian|date=25 May 2006|title=Tube Alloys directorate (act. 1941–1945)|url=https://www.oxforddnb.com/display/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-93791|access-date=25 October 2023|language=en|doi=10.1093/ref:odnb/93791}}</ref><ref name="Vrobel-2020">{{Cite thesis |last=Vrobel |first=Daniel P. |title=Paul Dirac: The Atomic Centrifuge and the Tube Alloys Project |date=2020 |publisher=Florida State University |url=https://diginole.lib.fsu.edu/islandora/object/fsu:770703/datastream/PDF/view |degree=Master}}</ref> Dirac made fundamental contributions to the process of [[Enriched uranium|uranium enrichment]] and the [[gas centrifuge]].<ref>{{Cite web |last=McKie |first=Robin |author-link=Robin McKie |date=31 January 2009 |title=Anti-matter and madness |url=https://www.theguardian.com/books/2009/feb/01/strangest-man-paul-dirac-review |access-date=24 October 2023 |website=amp.theguardian.com}}</ref><ref>{{Cite journal |last=Kemp |first=R. Scott |date=26 June 2009 |title=Gas Centrifuge Theory and Development: A Review of U.S. Programs |journal=Science & Global Security |language=en |volume=17 |issue=1 |pages=1–19 |doi=10.1080/08929880802335816 |issn=0892-9882|doi-access=free |bibcode=2009S&GS...17....1K }}</ref><ref>{{Cite journal |last=Gilinsky |first=Victor |date=2010 |title=Remembrances of Dirac |journal=Physics Today |volume=63 |issue=5 |page=59 |doi=10.1063/1.3431338|doi-access=free |bibcode=2010PhT....63e..59G }}</ref><ref name="Vrobel-2020" /> This work was deemed to be "probably the most important theoretical result in centrifuge technology".<ref>{{harvnb|Kragh|1990|p=158}}</ref>

===Gravity===
Dirac quantised the gravitational field.<ref name="Cern Courier-2002" /><ref name=Debnath/> His work laid the foundations for [[canonical quantum gravity]].<ref>{{Cite thesis |last=Schick |first=Michael |title=Canonical Quantum Gravity |date=2021 |publisher=Imperial College London |url=https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/theoretical-physics/msc/dissertations/2021/Michael-Schick-Dissertation.pdf |degree=}}</ref> 
In his 1959 lecture at the [[Lindau Nobel Laureate Meetings|Lindau Meetings]], Dirac discussed why [[gravitational wave]]s have "physical significance".<ref>{{Cite news |last=Skuse |first=Ben |date=1 September 2022 |title=Black Holes - Topic {{!}} Lindau Mediatheque |url=https://mediatheque.lindau-nobel.org/topics/black-holes |access-date=2 November 2023 |website=Lindau Nobel Mediatheque |language=en}}</ref> Dirac predicted gravitational waves would have well defined energy density in 1964.<ref name=Debnath>{{Cite journal |last=Debnath |first=Lokenath |author-link=Lokenath Debnath |date=2013 |title=A short biography of Paul A. M. Dirac and historical development of Dirac delta function |url=http://www.tandfonline.com/doi/abs/10.1080/0020739X.2013.770091 |journal=International Journal of Mathematical Education in Science and Technology |language=en |volume=44 |issue=8 |pages=1201–1223 |doi=10.1080/0020739X.2013.770091 |bibcode=2013IJMES..44.1201D |s2cid=121423215 |issn=0020-739X|url-access=subscription }}</ref> Dirac reintroduced the term "[[graviton]]" in a number of lectures in 1959, noting that the energy of the gravitational field should come in quanta.<ref>{{harvnb|Farmelo|2009|pp=367–368}}</ref><ref>{{Cite journal |last=Debnath |first=Lokenath |date=2013 |title=A short biography of Paul A. M. Dirac and historical development of Dirac delta function |url=http://www.tandfonline.com/doi/abs/10.1080/0020739X.2013.770091 |journal=International Journal of Mathematical Education in Science and Technology |language=en |volume=44 |issue=8 |pages=1201–1223 |doi=10.1080/0020739X.2013.770091 |bibcode=2013IJMES..44.1201D |s2cid=121423215 |issn=0020-739X|url-access=subscription }}</ref>

=== Cosmology ===
Dirac contributed to [[cosmology]], putting forth his [[Dirac large numbers hypothesis|large numbers hypothesis]].<ref>{{Cite journal |last=Dirac |first=Paul Adrien Maurice |date=5 April 1938 |title=A new basis for cosmology |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1938.0053 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |language=en |volume=165 |issue=921 |pages=199–208 |doi=10.1098/rspa.1938.0053 |bibcode=1938RSPSA.165..199D |s2cid=121069801 |issn=0080-4630|url-access=subscription }}</ref><ref>{{Cite journal |last=Kragh |first=Helge |date=2014 |title=Paul Dirac and the Magic of Large Numbers |url=https://academic.oup.com/book/4223/chapter-abstract/146058250?redirectedFrom=fulltext |journal=Masters of the Universe: Conversations with Cosmologists of the Past |pages=217–237 |doi=10.1093/acprof:oso/9780198722892.003.0012 |isbn=978-0-19-872289-2 |via=Oxford Academic|url-access=subscription }}</ref><ref>{{Cite journal |last1=Saibal |first1=Ray |last2=Mukhopadhyay |first2=Utpal |last3=Ray |first3=Soham |last4=Bhattacharjee |first4=Arjak |date=2019 |title=Dirac's large number hypothesis: A journey from concept to implication |url=https://www.worldscientific.com/doi/10.1142/S0218271819300143 |journal=International Journal of Modern Physics D |volume=28 |issue=8 |pages=1930014–1930096 |doi=10.1142/S0218271819300143 |bibcode=2019IJMPD..2830014R |s2cid=127899548 |via=World Scientific|url-access=subscription }}</ref><ref>{{Cite journal |last1=Dubois |first1=Eve-Aline |last2=Füzfa |first2=André |last3=Lambert |first3=Dominique |date=2022 |title=The large numbers hypothesis in cosmology |journal=The Fifteenth Marcel Grossmann Meeting |language=en |publisher=WORLD SCIENTIFIC |pages=1741–1744 |doi=10.1142/9789811258251_0259 |bibcode=2022mgm..conf.1741D |isbn=978-981-12-5824-4|s2cid=225097737 |doi-access=free }}</ref>

=== String theory ===
Dirac is seen as having anticipated [[string theory]], with his work on the [[Dirac membrane]] and [[Born–Infeld model|Dirac–Born–Infeld action]], both of which he proposed in a 1962 paper,<ref>{{Cite journal |date=1962-06-19 |title=An extensible model of the electron |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1962.0124 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |language=en |volume=268 |issue=1332 |pages=57–67 |doi=10.1098/rspa.1962.0124 |bibcode=1962RSPSA.268...57D |issn=0080-4630 |last1=Dirac |first1=P. A. M. |url-access=subscription }}</ref><ref>{{Cite web |title=membrane in nLab |url=https://ncatlab.org/nlab/show/membrane |access-date=2024-06-19 |website=ncatlab.org}}</ref> along with other contributions.<ref name="Kragh 1990-2">{{harvnb|Kragh|1990|pp=198, 348}}</ref><ref name="Sanyuk-2003">{{Cite journal |last1=Sanyuk |first1=Valerii I. |last2=Sukhanov |first2=Alexander D. |date=1 September 2003 |title=Dirac in 20th century physics: a centenary assessment |url=https://ufn.ru/en/articles/2003/9/c/ |journal=Physics-Uspekhi |language=en |volume=46 |issue=9 |pages=937–956 |doi=10.1070/PU2003v046n09ABEH001165 |s2cid=250754932 |issn=1063-7869|url-access=subscription }}</ref> He also developed a general theory of the quantum field with dynamical constraints,<ref>{{Cite journal |last=Dirac |first=P. A. M. |date=1950 |title=Generalized Hamiltonian Dynamics |journal=Canadian Journal of Mathematics |language=en |volume=2 |pages=129–148 |doi=10.4153/CJM-1950-012-1 |issn=0008-414X|doi-access=free }}</ref><ref>{{Cite journal |last=Dirac |first=P. A. M. |date=1951 |title=The Hamiltonian Form of Field Dynamics |journal=Canadian Journal of Mathematics |language=en |volume=3 |pages=1–23 |doi=10.4153/CJM-1951-001-2 |issn=0008-414X|doi-access=free }}</ref><ref name="Kragh 1990-2" /> which forms the basis of the [[Gauge theory|gauge theories]] and [[Superstring theory|superstring theories]] of today.<ref name="Kragh 1990-2" /><ref name="Cern Courier-2002" /><ref>[[Mikhail Shifman|Misha, S.]], ''Quantum Field Theory II'' ([[Singapore]]: [[World Scientific]], 2019), [https://books.google.com/books?id=EbySDwAAQBAJ&pg=PA287 p. 287].</ref><ref>{{Cite journal |last=Han |first=Xiaosen |date=2016-04-01 |title=The Born–Infeld vortices induced from a generalized Higgs mechanism |journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |language=en |volume=472 |issue=2188 |article-number=20160012 |doi=10.1098/rspa.2016.0012 |issn=1364-5021 |pmc=4892282 |pmid=27274694|bibcode=2016RSPSA.47260012H }}</ref><ref>{{Cite web |title=Biographical and Research Highlights |url=https://www.damtp.cam.ac.uk/events/dirac/dirac/highlights.html |access-date=2024-06-21 |website=Department of Applied Mathematics and Theoretical Physics (DAMTP)}}</ref>

===Other work===
Dirac wrote an influential paper in 1933 regarding the [[Lagrangian (physics)|Lagrangian]] in quantum mechanics.{{refn|Dirac's paper "THE LAGRANGIAN IN QUANTUM MECHANICS" is reprinted in {{harvnb|Feynman|Brown|2005}}}} The paper served as the basis for [[Julian Schwinger]] and his [[Schwinger's quantum action principle|quantum action principle]],{{sfn|Schweber|1994|pp=354, 573}} and laid the foundations for [[Richard Feynman]]'s development of a completely new approach to quantum mechanics, the [[path integral formulation]].<ref name="Debnath" /><ref>{{Cite book |last1=Baulieu |first1=Laurent |title=From Classical to Quantum Fields |last2=Iliopoulos |first2=John |author-link2=John Iliopoulos |last3=Sénéor |first3=Roland |publisher=[[Oxford University Press]] |year=2017 |isbn=978-0-19-878839-3 |edition=1st |page=164 |language=en}}</ref>

In a 1963 paper,<ref>{{Cite journal |last=Dirac |first=Paul |date=1963 |title=A Remarkable Representation of the 3 + 2 de Sitter Group |url=https://pubs.aip.org/aip/jmp/article-abstract/4/7/901/230214/A-Remarkable-Representation-of-the-3-2-de-Sitter?redirectedFrom=fulltext |journal=Journal of Mathematical Physics |publisher=AIP Publishing |volume=4 |issue=7 |pages=901–909|doi=10.1063/1.1704016 |bibcode=1963JMP.....4..901D |url-access=subscription }}</ref> Dirac initiated the study of field theory on [[Anti-de Sitter space|anti-de Sitter space (AdS)]].<ref>{{Cite journal |last1=Mezincescu |first1=Luca |last2=Townsend |first2=Paul K. |date=2020 |title=DBI in the IR |journal=Journal of Physics A: Mathematical and Theoretical |language=en |volume=53 |issue=4 |page=044002 |doi=10.1088/1751-8121/ab5eab |issn=1751-8121|arxiv=1907.06036 |bibcode=2020JPhA...53d4002M }}</ref> The paper contains the mathematics of combining special relativity with the quantum mechanics of quarks inside hadrons, and lays the foundations of [[Squeezed coherent state|two-mode squeezed states]] that are essential to [[Quantum optics|modern quantum optics]], though Dirac did not realize it at the time.<ref>{{Cite journal |last1=Kim |first1=Y S |last2=Noz |first2=Marilyn E |date=2005-12-01 |title=Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators |url=https://iopscience.iop.org/article/10.1088/1464-4266/7/12/005 |journal=Journal of Optics B: Quantum and Semiclassical Optics |volume=7 |issue=12 |pages=S458–S467 |doi=10.1088/1464-4266/7/12/005 |issn=1464-4266|arxiv=quant-ph/0502096 |bibcode=2005JOptB...7..458K }}</ref> Dirac previously worked on AdS during the 1930s,<ref>{{Cite book |last1=de Wit |first1=Bernard |last2=Herger |first2=Ivan |chapter=Anti-de Sitter Supersymmetry |date=2000 |editor-last=Kowalski-Glikman |editor-first=Jerzy |title=Towards Quantum Gravity |chapter-url=https://link.springer.com/chapter/10.1007/3-540-46634-7_4 |series=Lecture Notes in Physics |volume=541 |language=en |location=Berlin, Heidelberg |publisher=Springer |pages=79–100 |doi=10.1007/3-540-46634-7_4 |arxiv=hep-th/9908005 |isbn=978-3-540-46634-5}}</ref> publishing a paper in 1935.<ref>{{Cite journal |last=Dirac |first=P. A. M. |date=1935 |title=The Electron Wave Equation in De-Sitter Space |journal=Annals of Mathematics |volume=36 |issue=3 |pages=657–669 |doi=10.2307/1968649 |jstor=1968649 |issn=0003-486X}}</ref>

In 1930, [[Victor Weisskopf]] and [[Eugene Wigner]] published their famous and now standard calculation of spontaneous radiation emission in atomic and molecular physics.<ref>{{Cite journal |last1=Stenholm |first1=Stig Torsten |last2=Suominen |first2=Kalle-Antti |date=1998-04-27 |title=Weisskopf-Wigner decay of excited oscillator states |url=https://opg.optica.org/oe/abstract.cfm?uri=oe-2-9-378 |journal=Optics Express |language=en |volume=2 |issue=9 |pages=378–390 |doi=10.1364/OE.2.000378 |pmid=19381205 |bibcode=1998OExpr...2..378S |issn=1094-4087|doi-access=free }}</ref> Remarkably, in a letter to [[Niels Bohr]] in February 1927, Dirac had come to the same calculation,{{sfn|Schweber|1994|pp=31–32}} but he did not publish it.<ref>{{harvnb|Kragh|1990|p=125}}</ref>

In 1938,<ref>{{Cite journal |last=Dirac |first=P. A. M. |date=1938-08-05 |title=Classical Theory of Radiating Electrons |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1938.0124 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |language=en |volume=167 |issue=929 |pages=148–169 |doi=10.1098/rspa.1938.0124 |bibcode=1938RSPSA.167..148D |issn=0080-4630|url-access=subscription }}</ref> Dirac renormalized the mass in the theory of Abraham-Lorentz electron, leading to the [[Abraham–Lorentz force#Abraham–Lorentz–Dirac force|Abraham–Lorentz–Dirac force]], which is the relativistic-classical electron model; however, this model has solutions that suggest force increase exponentially with time.<ref>{{Cite journal |last1=Seto |first1=K. |last2=Zhang |first2=S. |last3=Koga |first3=J. |last4=Nagatomo |first4=H. |last5=Nakai |first5=M. |last6=Mima |first6=K. |date=2014-04-01 |title=Stabilization of radiation reaction with vacuum polarization |journal=Progress of Theoretical and Experimental Physics |volume=2014 |issue=4 |pages=43A01–0 |doi=10.1093/ptep/ptu031 |issn=2050-3911|arxiv=1310.6646 }}</ref>

[[Fermi's golden rule]], the formula for computing quantum transitions in time dependent systems, declared a "golden rule" by [[Enrico Fermi]], was derived by Dirac.<ref>{{Cite book |last=Jena |first=Debdeep |url=https://academic.oup.com/book/43800/chapter/370780511 |title=Fermi's Golden Rule |date=2022-05-26 |publisher=Oxford University PressOxford |isbn=978-0-19-885684-9 |edition=1 |pages=461–480 |language=en |doi=10.1093/oso/9780198856849.003.0020}}</ref> Dirac was the one to initiate the development of [[Perturbation theory (quantum mechanics)#Time-dependent perturbation theory|time-dependent perturbation theory]] in his early work on semi-classical atoms interacting with an electromagnetic field. Dirac, with [[Werner Heisenberg]], [[John Archibald Wheeler]], Richard Feynman, and [[Freeman Dyson]] ultimately developed this concept into an invaluable tool for modern physics, used in the calculation of the properties of any physical system and a wide array of phenomena.<ref>{{Cite book |last1=Geddes |first1=Chris D. |url=https://books.google.com/books?id=WJUrPL4FZsAC&dq=Fermi%27s+golden+rule+dirac&pg=PA38 |title=Reviews in Fluorescence 2006 |last2=Lakowicz |first2=Joseph R. |publisher=Springer Science+Business Media, Inc. Springer e-books |year=2006 |isbn=978-0-387-33016-7 |location=Boston, MA}}</ref>

==Career==
===University of Cambridge===
From 1932 to 1969, Dirac was the [[Lucasian Professor of Mathematics]] at the [[University of Cambridge]]. In 1934, He conceived the [[Helikon vortex separation process|Helikon vortex isotope separation process]].<ref>{{Citation |last=Kaufmann |first=André |title=Useful Applications of the RHVT |date=2022 |work=The Ranque Hilsch Vortex Tube Demystified: Understanding the Working Principles of the Vortex Tube |page=69 |editor-last=Kaufmann |editor-first=André |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-89766-6_6 |isbn=978-3-030-89766-6|doi-access=free }}</ref><ref>{{harvnb|Farmelo|2009|pp=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA248 248–249]}} quote=During a visit to Cambridge in May 1934, Wigner saw the apparatus and asked Dirac questions about it,</ref> In 1937, he proposed a speculative [[Physical cosmology|cosmological]] model based on the [[Dirac large numbers hypothesis|large numbers hypothesis]]. During World War II, he conducted important theoretical work on [[uranium enrichment]] by [[gas centrifuge]].<ref>Kemp, R. S., [https://www.researchgate.net/publication/228424622_Gas_Centrifuge_Theory_and_Development_A_Review_of_US_Programs "Gas Centrifuge Theory and Development: A Review of US Programs"], ''Science and Global Security'', June 2009.</ref> He introduced the [[Separative work units|separative work unit]] (SWU) in 1941.<ref>{{cite arXiv |eprint=0906.2505 |class=physics.hist-ph |first=Jeremy |last=Bernstein |title=SWU for You and Me |date=13 June 2009}}</ref> He contributed to the [[Tube Alloys|Tube Alloys project]], the British programme to research and construct atomic bombs during World War II.<ref>{{Cite ODNB |last=Cathcart |first=Brian |date=25 May 2006 |title=Tube Alloys directorate (act. 1941–1945) |url=https://www.oxforddnb.com/display/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-93791 |access-date=25 October 2023 |language=en |doi=10.1093/ref:odnb/93791}}</ref><ref name="Vrobel-2020"/>

The Hamiltonian of constrained systems is one of Dirac's many masterpieces. It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by <math>g_{rs}</math>,<math>p^{rs}</math> for each point of the surface on which the state is considered. The  <math>g_{m0}</math> (''m'' = 0, 1, 2, 3) appear in the theory only through the variables <math>g^{r0}</math>, <math> ( -{g^{00}} ) ^{-1/2}</math> which occur as arbitrary coefficients in the equations of motion.
There are four constraints or weak equations for each point of the surface <math>x^0</math> = constant. Three of them <math>H_r</math> form the four vector density in the surface. The fourth <math>H_L</math> is a 3-dimensional scalar density in the surface ''H''<sub>L</sub> ≈ 0; ''H<sub>r</sub>'' ≈ 0 (''r'' = 1, 2, 3).<ref>{{cite journal |last1=Dirac |first1=P. A. M. |title=Generalized Hamiltonian Dynamics |journal=Canadian Journal of Mathematics |date=January 1950 |volume=2 |pages=129–148 |doi=10.4153/CJM-1950-012-1 |url=https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/generalized-hamiltonian-dynamics/F4C30A59B59BEE09E9CB6F07377B8BD3 |language=en |issn=0008-414X}}</ref>

In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein's [[general relativity]] in Hamiltonian form<ref>{{Cite journal |date=1958-08-19 |title=The theory of gravitation in Hamiltonian form |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1958.0142 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |language=en |volume=246 |issue=1246 |pages=333–343 |doi=10.1098/rspa.1958.0142 |bibcode=1958RSPSA.246..333D |issn=0080-4630 |last1=Dirac |first1=P. A. M. |url-access=subscription }}</ref><ref>{{cite journal |last1=Dirac |first1=P. A. M. |title=Fixation of Coordinates in the Hamiltonian Theory of Gravitation |journal=Physical Review |date=1 May 1959 |volume=114 |issue=3 |page=924 |doi=10.1103/PhysRev.114.924 |bibcode=1959PhRv..114..924D |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.114.924 |access-date=16 October 2020}}</ref> and to bring to a technical completion the quantisation problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society.<ref>Dirac, P. A. M., [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.2.368 "Energy of the Gravitational Field"], ''[[Physical Review Letters]]'', Vol. 2, Nr. 8, 20 March 1959, pp. 368–371.</ref> In 1964 he published his ''Lectures on Quantum Mechanics'' (London: Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantisation of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.

The 1963–1964 lectures Dirac gave on quantum field theory at [[Yeshiva University]] were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3.

===Florida State University and University of Miami===
[[File:Paul Dirac Bust at FSU.jpg|thumb|upright|A bust of Paul Dirac at Florida State University]]
In 1969, Dirac was forced to retire from his chair at Cambridge, due to his age (67).<ref>{{Cite book |last=Kragh |first=Helge |url=https://pressbooks.pub/simplydirac/ |title=Simply Dirac |publisher=Simply Charly |year=2016 |isbn=978-1-943657-00-1 |edition=ebook |publication-date=April 29, 2016}}</ref> Before his retirement he was offered a visiting position at the [[University of Miami]] in [[Coral Gables, Florida]]; he accepted, joining its newly formed [[Center for Theoretical Studies, University of Miami|Center for Theoretical Studies]].<ref>{{Cite journal |date=April 1969 |title=Dirac Receives Miami Center Oppenheimer Memorial Prize |url=https://pubs.aip.org/physicstoday/article-abstract/22/4/127/426774/Dirac-Receives-Miami-Center-Oppenheimer-Memorial |journal=[[Physics Today]] |volume=22 |issue=4 |pages=127–128|doi=10.1063/1.3035512 |url-access=subscription }}</ref> In September 1970 he also accepted a visiting professor position at [[Florida State University]] in [[Tallahassee, Florida]], and moved his family to Tallahassee. He accepted a position at FSU as a full professor in 1972.<ref name="Diracmathshistory" /><ref>{{Cite web |last=Klopfenstein |first=Kelsey |date=2024-04-03 |title=How Paul Dirac's legacy brought a student from Nepal to FSU |url=https://news.fsu.edu/news/fsuglobal/2024/04/03/how-paul-diracs-legacy-brought-a-student-from-nepal-to-fsu/ |access-date=2024-07-29 |website=Florida State University News |language=en-US}}</ref>

Contemporary accounts of his time in Tallahassee describe it as happy, except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge.<ref>{{cite web|url=https://www.famousscientists.org/paul-dirac/|title=Paul Dirac|website=Famous Scientists|date=13 October 2021 }}</ref> He would walk about a mile to work each day and was fond of swimming in one of the two nearby lakes (Silver Lake and Lost Lake), and was also more sociable than he had been at the University of Cambridge, where he mostly worked at home apart from giving classes and seminars. At Florida State, he would usually eat lunch with his colleagues before taking a nap.<ref>{{Cite book|last=Pais|first=Abraham|url=https://books.google.com/books?id=Hm22wB0wGFcC|title=Paul Dirac: The Man and His Work|page=27|date=2009|publisher=Cambridge University Press|isbn=978-0-511-56431-4|oclc=958553083|via=Google Books}}</ref>

Dirac published over 60 papers at FSU during those last twelve years of his life, including a short book on general relativity.<ref>Baer, H. A., & Belyaev, A., eds., ''Proceedings of the Dirac Centennial Symposium'' (Singapore: World Scientific, 2003), [https://books.google.com/books?id=9RvJCgAAQBAJ&pg=PA3 p. 3].</ref> His last paper (1984), entitled "The inadequacies of quantum field theory," contains his final judgment on quantum field theory: "These rules of renormalisation give surprisingly, excessively good agreement with experiments. Most physicists say that these working rules are, therefore, correct. I feel that is not an adequate reason. Just because the results happen to be in agreement with observation does not prove that one's theory is correct." The paper ends with the words: "I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as I can and other people, I hope, will follow along such lines."<ref>{{Cite book|last=Pais|first=Abraham|url=https://books.google.com/books?id=Hm22wB0wGFcC|title=Paul Dirac: The Man and His Work|page=28|date=2009|publisher=Cambridge University Press|isbn=978-0-511-56431-4|oclc=958553083|via=Google Books}}</ref>

In 1975, Dirac gave a series of five lectures at the [[University of New South Wales]] which were subsequently published as a book, ''Directions in Physics'' (1978). He donated the royalties from this book to the university for the establishment of Dirac Lecture Series. The [[Dirac Medal (UNSW)|Silver Dirac Medal for the Advancement of Theoretical Physics]] is awarded by the University of New South Wales to commemorate the lecture.<ref>{{cite web |url=http://www.phys.unsw.edu.au/ANNUAL_REPORTS/2004/school7.html |title=Dirac Medal awards |publisher=University of New South Wales |access-date=4 April 2013 |archive-url=https://web.archive.org/web/20130412032421/http://www.phys.unsw.edu.au/ANNUAL_REPORTS/2004/school7.html |archive-date=12 April 2013 }}</ref>

===Students===
Amongst his many students<ref name="mathgene">{{MathGenealogy|id=18524}}</ref><ref name="mactutor">{{MacTutor Biography|id=Dirac}}</ref> were [[Homi J. Bhabha]],<ref name=bhabhaphd>{{cite thesis|degree=PhD|url=https://www.repository.cam.ac.uk/handle/1810/250819|title=On cosmic radiation and the creation and annihilation of positrons and electrons|first= Homi Jehangir|last=Bhabha|year=1935|id={{EThOS|uk.bl.ethos.727546}}|publisher=University of Cambridge}}</ref> [[Fred Hoyle]], [[John Polkinghorne]]<ref name=polking>{{cite thesis|degree=PhD|url=http://idiscover.lib.cam.ac.uk/primo-explore/fulldisplay?docid=44CAM_ALMA21428195830003606&context=L&vid=44CAM_PROD&search_scope=SCOP_CAM_ALL&tab=cam_lib_coll&lang=en_US|title=Contributions to quantum field theory|first= John Charlton|last=Polkinghorne|year=1955|id={{EThOS|uk.bl.ethos.727138}}|publisher=University of Cambridge}}</ref> and [[Freeman Dyson]].<ref>Sandberg, L., [https://www.ias.edu/press-releases/2020/freeman-j-dyson-1923–2020 "Freeman J. Dyson (1923–2020), Scientist and Writer, Who Dreamt Among the Stars, Dies at 96"], [[Institute for Advanced Study|IAS]], 28 February 2020.</ref> Polkinghorne recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."<ref>{{Cite book |last=Polkinghorne |first=John C. |title=Belief in God in an age of science |author-link=John Polkinghorne|date=2003 |publisher=Yale Nota Bene |isbn=978-0-300-09949-2 |series=Terry lecture series |location=New Haven, Conn. London}}</ref>{{rp|2}} In 1930, [[Subrahmanyan Chandrasekhar]] attended Dirac's course on quantum mechanics four times, describing it as "just like a piece of music you want to hear over and over again."{{sfnp| Farmelo| 2009| p=180}}

==Death and recognition==
[[File:Nima visits dirac.jpg|thumb|The tombstone of Dirac and his wife in Roselawn Cemetery, [[Tallahassee, Florida]]. Their daughter Mary Elizabeth Dirac, who died 20 January 2007, is buried next to them.]]
[[File:Dirac's commemorative marker.jpg|thumb|The commemorative marker in [[Westminster Abbey]]]]

Dirac died on 20 October 1984 in [[Tallahassee, Florida]], at the age of 82, and is buried at Tallahassee's Roselawn Cemetery.<ref name="Newton">{{cite web |url=http://www.fsu.edu/~fstime/FS-Times/Volume1/Issue1/Dirac.html |title=Dirac takes his place next to Isaac Newton |publisher=Florida State University |access-date=4 April 2013 |archive-url=https://web.archive.org/web/19970427191316/http://www.fsu.edu/~fstime/FS-Times/Volume1/Issue1/Dirac.html |archive-date=27 April 1997 }}</ref> Dirac's childhood home in [[Bishopston, Bristol]], is commemorated with a [[blue plaque]],<ref>Fells, M., ''Bristol Plaques'' ([[Cheltenham]]: [[The History Press]], 2016), [https://books.google.com/books?id=ezJIDAAAQBAJ&pg=PT40 p. 40].</ref> and the nearby Dirac Road is named in recognition of his links with the city of [[Bristol]]. A commemorative stone was erected in a garden in [[Saint-Maurice, Switzerland]], the town of origin of his father's family, on 1 August 1991. On 13 November 1995 a commemorative marker, made from Burlington green [[slate]] and inscribed with the [[Dirac equation]], was unveiled in [[Westminster Abbey]].<ref name = "Newton" /><ref>{{cite web |url=http://www.dirac.ch/PaulDirac.html |title= Paul Dirac |publisher=Gisela Dirac |access-date=4 April 2013}}</ref> The [[Dean of Westminster]], [[Edward Carpenter (priest)|Edward Carpenter]], had initially refused permission for the memorial, thinking Dirac to be anti-Christian, but was eventually (over a five-year period) persuaded to relent.<ref>{{harvnb|Farmelo|2009|pp=[https://books.google.com/books?id=-TT_z4llWoIC&pg=PA414 414–415]}}.</ref>

===Awards and honours===
Dirac shared the 1933 [[Nobel Prize in Physics]] with [[Erwin Schrödinger]] "for the discovery of new productive forms of atomic theory".<ref name =nobel/> He was the youngest ever theoretician to win the prize, at the age of 31, until [[Tsung-Dao Lee|T. D. Lee]] in 1957.<ref>{{Cite web |last=Farmelo |first=Graham | author-link=Graham Farmelo |date=2008 |title=Paul Dirac: The Mozart of Science |url=https://www.ias.edu/ideas/2008/farmelo-on-dirac |access-date=2024-05-08 |website=www.ias.edu |language=en}}</ref> Dirac was also awarded the [[Royal Medal]] in 1939 and both the [[Copley Medal]] and the [[Max Planck Medal]] in 1952. He was elected a Fellow of the [[Royal Society]] in 1930,<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-bio.html |title=Nobel Bio |publisher=Nobel Foundation |access-date=27 January 2014}}</ref><ref name="frs"/> a member of the [[American Philosophical Society]] in 1938,<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Paul+Dirac&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=16 May 2023 |website=search.amphilsoc.org}}</ref> an Honorary Fellow of the [[American Physical Society]] in 1948, a member of the United States [[National Academy of Sciences]] in 1949,<ref>{{Cite web |title=Paul A. Dirac |url=http://www.nasonline.org/member-directory/deceased-members/46802.html |access-date=16 May 2023 |website=www.nasonline.org}}</ref> a member of the [[American Academy of Arts and Sciences]] in 1950,<ref>{{Cite web |date=9 February 2023 |title=Paul Adrien Maurice Dirac |url=https://www.amacad.org/person/paul-adrien-maurice-dirac |access-date=16 May 2023 |website=American Academy of Arts & Sciences |language=en}}</ref> and an Honorary Fellow of the [[Institute of Physics]], London in 1971. He received the inaugural [[J. Robert Oppenheimer Memorial Prize]] in 1969.<ref>{{cite book| title= Winners, the blue ribbon encyclopedia of awards | url= https://archive.org/details/winnersblueribbo0000walt | url-access= registration |last=Walter |first=Claire |year=1982 |page= [https://archive.org/details/winnersblueribbo0000walt/page/438 438]|publisher=Facts on File Inc.|isbn=978-0-87196-386-4 }}</ref><ref>{{cite journal |author=<!--Staff writer(s); no by-line.--> |title=Dirac Receives Miami Center Oppenheimer Memorial Prize |journal=Physics Today |volume=22 |issue=4 |date=April 1969 |page=127 |doi=10.1063/1.3035512 }}</ref> Dirac became a member of the [[Order of Merit]] in 1973, having previously turned down a [[knight]]hood as he did not want to be addressed by his first name.<ref name="mckie"/><ref>{{harvnb|Farmelo|2009|pp=403–404}}</ref>

After his death, two organisations of professional physicists established annual awards in Dirac's memory. The [[Institute of Physics]], the United Kingdom's professional body for physicists, awards the [[Dirac Medal (IOP)|Paul Dirac Medal]] for "outstanding contributions to theoretical (including mathematical and computational) physics".<ref>{{cite web |url=http://www.iop.org/about/awards/gold/dirac/page_38427.html |title=The Dirac Medal | publisher=[[Institute of Physics]] | access-date=24 November 2007}}</ref> The first three recipients were [[Stephen Hawking]] (1987), [[John Stewart Bell]] (1988), and [[Roger Penrose]] (1989). Since 1985, the [[International Centre for Theoretical Physics]] awards the [[Dirac Medal (ICTP)|Dirac Medal of the ICTP]] each year on Dirac's birthday (8 August).<ref>{{cite web |url=http://www.ictp.it/about-ictp/prizes-awards/the-dirac-medal.aspx |title=The Dirac Medal |publisher=International Centre for Theoretical Physics |access-date=4 April 2013}}</ref>

The Dirac–Hellman Award at [[Florida State University]] was endowed by Bruce P. Hellman in 1997 to reward outstanding work in theoretical physics by FSU researchers.<ref>{{cite web |url=http://www.physics.fsu.edu/undergrads/UndergraduateAwards.htm |title=Undergraduate Awards |publisher=Florida State University |access-date=4 April 2013 |archive-url=https://web.archive.org/web/20130412191942/http://www.physics.fsu.edu/undergrads/UndergraduateAwards.htm |archive-date=12 April 2013 }}</ref> The Paul A.M. Dirac Science Library at Florida State University, which Manci opened in December 1989,<ref>{{cite web|title=Remodelled Dirac Science Library Opened at FSU|url=http://grahamfarmelo.com/remodelled-dirac-science-library-formally-opened-at-fsu/|publisher=Graham Farmelo|access-date=12 October 2015|date=22 February 2015}}</ref> is named in his honour, and his papers are held there.<ref>{{cite web|url=http://purl.fcla.edu/fsu/MSS_1989-009 |title=Paul A.M. Dirac Papers |publisher=Florida State University |access-date=18 March 2021 }}</ref> Outside is a statue of him by Gabriella Bollobás.<ref>{{harvnb|Farmelo|2009|p=417}}</ref> The street on which the [[National High Magnetic Field Laboratory]] in Innovation Park of Tallahassee, Florida, is located is named Paul Dirac Drive. As well as in his hometown of Bristol, there is also a road named after him, Dirac Place, in [[Didcot]], Oxfordshire.<ref>{{cite web|url=https://www.google.co.uk/maps/place/Dirac+Pl,+Didcot+OX11+8TL/@51.6019901,-1.2359636,17z/data=!3m1!4b1!4m5!3m4!1s0x4876beade0b4889f:0xa7b8fb34ab4aaa78!8m2!3d51.6019901!4d-1.2337749|title=Dirac Place, Didcot OX11 8TL|publisher=Google Maps}}</ref> The Dirac-Higgs Science Centre in Bristol is also named in his honour.<ref>{{cite news | url=https://www.theguardian.com/education/2015/jan/29/bristol-cotham-school-scores-exam-results-famous-alumni-peter-higgs-paul-dirac | title=Bristol's Cotham school scores exam results to outshine famous alumni | newspaper=The Guardian | date=29 January 2015 | last1=Weale | first1=Sally }}</ref>

The BBC named a [[video codec]], [[Dirac (video compression format)|Dirac]], in his honour. An [[5997 Dirac|asteroid]] discovered in 1983 was named after Dirac.<ref name="5997dirac">{{cite web |url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=5997+Dirac |title= 5997 Dirac (1983 TH) | publisher=Jet Propulsion Laboratory |access-date=9 January 2015}}</ref> The Distributed Research utilising Advanced Computing ([[DiRAC]]) and [[Dirac (software)|Dirac]] software are named in his honour.

=== Praise ===
Dirac is widely considered to be on par with [[Isaac Newton]], [[James Clerk Maxwell]], and [[Albert Einstein]].<ref>{{Cite book |last1=Hey |first1=Tony |author-link=Tony Hey |url=https://archive.org/details/quantumuniverse0000heya/page/124 |title=The Quantum Universe |last2=Walters |first2=Patrick |publisher=Cambridge University Press |year=1987 |isbn=978-0-521-26744-1 |pages=124 |language=en}}</ref><ref>{{Cite journal |last=Close |first=Frank |date=20 May 2009 |title=Paul Dirac: a physicist of few words |journal=Nature |language=en |volume=459 |issue=7245 |pages=326–327 |doi=10.1038/459326a |issn=1476-4687|doi-access=free |bibcode=2009Natur.459..326C }}</ref>{{sfn|Kragh|1990|pp=ix, 12}} Einstein wrote that to Dirac "we owe the most logically perfect presentation of [quantum mechanics]."<ref>{{cite book| last=Pais| first=Abraham| title=[[Subtle is the Lord: The Science and the Life of Albert Einstein]]| year=1982| page=441}}</ref>

On the occasion of the 100th anniversary of Dirac's birth, [[Richard Dalitz]] wrote "The influence and importance of Dirac's work have increased with the decades, and physicists use daily the concepts and equations that he developed."<ref name="Cern Courier-2002" />

In [[Lev Landau]]'s [[Lev Landau#Landau's ranking of physicists|logarithmic scale]] of physicists from 0 to 5 based on productivity and genius, (0 being the highest and 5 the lowest) he ranked Dirac a 1, along with other fathers of quantum mechanics such as Schrödinger and [[Werner Heisenberg]].<ref>{{Cite journal |last1=Li |first1=Jichao |last2=Yin |first2=Yian |last3=Fortunato |first3=Santo |last4=Wang |first4=Dashun |date=2019-04-18 |title=Nobel laureates are almost the same as us |url=https://www.nature.com/articles/s42254-019-0057-z |journal=Nature Reviews Physics |language=en |volume=1 |issue=5 |pages=301–303 |doi=10.1038/s42254-019-0057-z |bibcode=2019NatRP...1..301L |issn=2522-5820|url-access=subscription }}</ref>

[[John Polkinghorne]] wrote: "Not only was Dirac the greatest theoretical physicist known to me personally, his purity of spirt and modesty of demeanour (he never emphasized in the slightest degree his own immense contributions to the fundamentals of the subject) made him an inspiring figure and a kind of scientific saint."<ref>{{cite book| last=Polkinghorne| first=John| author-link=John Polkinghorne| title=Quantum Theory: A Very Short Introduction| publisher=Oxford University Press}}</ref>{{rp|xii}}

==Books==
* ''[[The Principles of Quantum Mechanics]]'' (1930): This book summarises the ideas of quantum mechanics using the modern formalism that was largely developed by Dirac himself. Towards the end of the book, he also discusses the relativistic theory of the electron (the [[Dirac equation]]), which was also pioneered by him. This work does not refer to any other writings then available on quantum mechanics.
* ''Lectures on Quantum Mechanics'' (1966): Much of this book deals with quantum mechanics in [[curved space-time]].
* ''Lectures on Quantum Field Theory'' (1966): This book lays down the foundations of [[quantum field theory]] using the [[Hamiltonian mechanics|Hamiltonian]] formalism.
* ''Spinors in Hilbert Space'' (1974): This book based on lectures given in 1969 at the University of Miami deals with the basic aspects of [[spinor]]s starting with a real [[Hilbert space]] formalism.
* ''General Theory of Relativity'' (1975): Based on Dirac's 1975 lectures at Florida State University, this 69-page work summarises Einstein's general theory of relativity.<ref>{{Cite book |last=Dirac |first=P. A. M. |title=General Theory of Relativity |date=2016 |publisher=Princeton University Press |isbn=978-0-691-01146-2 |series=Physics Notes |location=Princeton, NJ}}</ref>

==References==
=== Citations ===
{{Reflist}}

=== General sources ===
{{refbegin|30em}}
* {{cite book |last=Capri |first=Anton Z. |year=2007 |title=Quips, Quotes, and Quanta: An Anecdotal History of Physics |publisher=World Scientific |location=Hackensack, New Jersey |isbn=978-981-270-919-6 |url=https://books.google.com/books?id=GfmR0mHxeZkC&pg=PA148 |oclc=214286147}}
* {{cite book |last1=Crease |first1=Robert P. |author-link1=Robert P. Crease |last2=Mann |first2=Charles C. |author-link2=Charles C. Mann |year=1986 |title=The Second Creation: Makers of the Revolution in Twentieth Century Physics |publisher=Macmillan Publishing |location=New York City |isbn=978-0-02-521440-8 |oclc=13008048|url=https://archive.org/details/secondcreationma00crea}}
* {{cite book |last=Farmelo |first=Graham |author-link=Graham Farmelo |year=2009 |title=[[The Strangest Man|The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius]] |location=London |publisher=Faber and Faber |isbn=978-0-571-22278-0}} [Published in the United States as ''The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom''. {{isbn|978-0-465-01827-7}}.]
* {{Cite book |last1=Feynman |first1=Richard P. |url=https://www.worldcat.org/title/ocm62332166 |title=Feynman's thesis: a new approach to quantum theory |last2=Brown |first2=Laurie M. |date=2005 |publisher=World Scientific |isbn=978-981-256-366-8 |location=Hackensack, NJ |oclc=ocm62332166}}
* {{cite book |last=Gamow |first=George |author-link=George Gamow |year=1966 |title=Thirty Years That Shook Physics: The Story of Quantum Theory |publisher=Doubleday |location=Garden City, New York |isbn=978-0-486-24895-0 |url = https://books.google.com/books?id=L90_wY1VCW0C&pg=PA121 |oclc=11970045}}
* {{cite book |last=Heisenberg |first=Werner |author-link=Werner Heisenberg |title=Physics and Beyond: Encounters and Conversations |publisher=Harper & Row |location=New York City |isbn=978-0-06-131622-7 |year=1971 |oclc=115992|url=https://archive.org/details/physicsbeyondenc00heis }}
* {{cite book |last=Kragh |first=Helge |author-link=Helge Kragh |title=Dirac: A Scientific Biography |year=1990 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-38089-8 |oclc=20013981 |url=https://archive.org/details/diracscientificb0000krag |url-access=registration}}
* {{cite book |last=Mehra |first=Jagdish |author-link=Jagdish Mehra |contribution=The Golden Age of Theoretical Physics: P. A. M. Dirac's Scientific Works from 1924–1933 |editor-last=Wigner |editor-first=Eugene Paul |editor-link=Eugene Wigner |editor2-last=Salam |editor2-first=Abdus |editor2-link=Abdus Salam |year=1972 |title=Aspects of Quantum Theory |pages=17–59 |publisher=University Press |location=Cambridge |isbn=978-0-521-08600-4 |oclc=532357}}
* {{cite book |last=Schweber |first=Silvan S. |author-link=Silvan S. Schweber |title=QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga |url=https://archive.org/details/qedmenwhomadeitd0000schw |url-access=registration |publisher=Princeton University Press |location=Princeton, New Jersey |year= 1994 |isbn=978-0-691-03685-4 |oclc=28966591}}
* {{cite book |last=Zee |first=Anthony |author-link=Anthony Zee |title=Quantum Field Theory in a Nutshell |url=https://archive.org/details/isbn_9780691140346|url-access=registration |publisher=Princeton University Press |location=Princeton, New Jersey |year=2010 |oclc=318585662| isbn=978-1-4008-3532-4}}
{{refend}}

== Further reading ==
* {{Cite news |last=Brown|first=Helen|title=The Strangest Man: The Hidden Life of Paul Dirac by Graham Farmelo – review &#91;print version: The man behind the maths&#93; |url=https://www.telegraph.co.uk/culture/books/bookreviews/4316309/The-Strangest-Man-the-Hidden-Life-of-Paul-Dirac-by-Graham-Farmelo---review.html |archive-url=https://web.archive.org/web/20090202082203/http://www.telegraph.co.uk/culture/books/bookreviews/4316309/The-Strangest-Man-the-Hidden-Life-of-Paul-Dirac-by-Graham-Farmelo---review.html |archive-date=2 February 2009 |newspaper=[[The Daily Telegraph]] (Review)|date=24 January 2009|page=20 |access-date=11 April 2011}}.
* {{Cite news |last=Gilder |first=Louisa |title=Quantum Leap – Review of 'The Strangest Man: The Hidden Life of Paul Dirac by Graham Farmelo'|url=https://www.nytimes.com/2009/09/13/books/review/Gilder-t.html |newspaper=[[The New York Times]] |date=13 September 2009 |access-date=11 April 2011}} Review.
* Mukunda, N. (1987) "The life and work of P.A.M. Dirac", pages 260 to 282 in ''Recent Developments in Theoretical Physics'', [[World Scientific]] {{mr|id=935624}}

== External links ==
{{Commons and category|Paul Dirac}}
{{wikiquote}}
* [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575-1 Oral history interview transcript with P. A. M. Dirac on 1 April 1962, American Institute of Physics, Niels Bohr Library & Archives]—Session I
* [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575-2 Oral history interview transcript with P. A. M. Dirac on 6 May 1963, American Institute of Physics, Niels Bohr Library & Archives]—Session II
* [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575-3 Oral history interview transcript with P. A. M. Dirac on 7 Mary 1963, American Institute of Physics, Niels Bohr Library & Archives]—Session III
* [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575-4 Oral history interview transcript with P. A. M. Dirac on 10 May 1963, American Institute of Physics, Niels Bohr Library & Archives]—Session IV
* [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575-5 Oral history interview transcript with P. A. M. Dirac on 14 May 1963, American Institute of Physics, Niels Bohr Library & Archives]—Session V
* [https://royalsocietypublishing.org/action/doSearch?field1=Contrib&text1=Dirac&ConceptID=&ConceptID=&publication=&Ppub=&access=on Free online access to Dirac's classic 1920s papers from Royal Society's Proceedings A]
* [https://web.archive.org/web/20190502044245/http://alsos.wlu.edu/qsearch.aspx?browse=people%2FDirac%2C+Paul Annotated bibliography for Paul Dirac from the Alsos Digital Library for Nuclear Issues]
* [http://purl.fcla.edu/fsu/MSS_1989-009 The Paul Dirac Collection at Florida State University]
* [https://archivesearch.lib.cam.ac.uk/repositories/9/resources/1531 The Papers of Professor Paul Dirac] at the [[Churchill Archives Centre]]
* [https://www.youtube.com/watch?v=fWo010EsiYk Oral history interview with Steve Edwards and Joe Lannutti on Dirac's appointment at Florida State University]

{{Copley Medallists 1951-2000}}
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