Editing Paul Dirac (section)

===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.