Editing Paul Dirac (section)

===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 |pages=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 }}</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 |url=https://dx.doi.org/10.1088/1751-8121/ab5eab |journal=Journal of Physics A: Mathematical and Theoretical |language=en |volume=53 |issue=4 |pages=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 |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 |url=https://www.jstor.org/stable/1968649 |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}}</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 |url=https://doi.org/10.1093/ptep/ptu031 |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>