Editing Paul Dirac (section)

==Academia==
===University of Cambridge===
Dirac was the [[Lucasian Professor of Mathematics]] at the [[University of Cambridge]] from 1932 to 1969. He conceived the [[Helikon vortex separation process|Helikon vortex isotope separation process]] in 1934.<ref>{{Citation |last=Kaufmann |first=André |title=Useful Applications of the RHVT |date=2022 |url=https://doi.org/10.1007/978-3-030-89766-6_6 |work=The Ranque Hilsch Vortex Tube Demystified: Understanding the Working Principles of the Vortex Tube |pages=69 |editor-last=Kaufmann |editor-first=André |access-date=11 January 2024 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-89766-6_6 |isbn=978-3-030-89766-6}}</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.{{citation needed|date=July 2024}} 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)

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. }}</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 }}</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 |url-status=dead |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/> [[Fred Hoyle]], [[John Polkinghorne]]<ref name=polking/> 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}}