Editing Richard Feynman (section)

== Cornell (1945–1949) ==
Feynman nominally held an appointment at the [[University of Wisconsin–Madison]] as an assistant professor of physics, but was on unpaid leave during his involvement in the Manhattan Project.{{sfn|Gribbin|Gribbin|1997|p=101}} In 1945, he received a letter from Dean Mark Ingraham of the College of Letters and Science requesting his return to the university to teach in the coming academic year. His appointment was not extended when he did not commit to returning. In a talk given there several years later, Feynman quipped, "It's great to be back at the only university that ever had the good sense to fire me."<ref>{{cite journal |author=March |first=Robert H. |year=2003 |title=Physics at the University of Wisconsin: A History |journal=Physics in Perspective |volume=5 |issue=2 |pages=130–149 |bibcode=2003PhP.....5..130M |doi=10.1007/s00016-003-0142-6 |s2cid=120730710}}</ref>

As early as October 30, 1943, Bethe had written to the chairman of the physics department of his university, [[Cornell University|Cornell]], to recommend that Feynman be hired. On February 28, 1944, this was endorsed by [[Robert Bacher]],{{sfn|Mehra|1994|pp=161–164, 178–179}} also from Cornell,{{sfn|Hoddeson|Henriksen|Meade|Westfall|1993|pp=47–52}} and one of the most senior scientists at Los Alamos.{{sfn|Hoddeson|Henriksen|Meade|Westfall|1993|p=316}} This led to an offer being made in August 1944, which Feynman accepted. Oppenheimer had also hoped to recruit Feynman to the University of California, but the head of the physics department, [[Raymond T. Birge]], was reluctant. He made Feynman an offer in May 1945, but Feynman turned it down. Cornell matched its salary offer of $3,900 ({{Inflation|US|3900|1945|fmt=eq|r=-3}}) per annum.{{sfn|Mehra|1994|pp=161–164, 178–179}} Feynman became one of the first of the Los Alamos Laboratory's group leaders to depart, leaving for [[Ithaca, New York]], in October 1945.{{sfn|Gleick|1992|p=205}}

Because Feynman was no longer working at the Los Alamos Laboratory, he was no longer exempt from [[the draft]]. At his induction physical, Army psychiatrists diagnosed Feynman as suffering from a mental illness and the Army gave him a [[Selective Service System#Classifications|4-F exemption]] on mental grounds.{{sfn|Gleick|1992|p=225}}{{sfn|Feynman|1985|pp=162–163}} His father died suddenly on October 8, 1946, and Feynman suffered from depression.{{sfn|Mehra|1994|pp=171–174}} On October 17, 1946, he wrote a letter to Arline, expressing his deep love and heartbreak. The letter was sealed and only opened after his death. "Please excuse my not mailing this," the letter concluded, "but I don't know your new address."<ref>{{cite web |title=I love my wife. My wife is dead. |date=February 15, 2012 |url=https://lettersofnote.com/2012/02/15/i-love-my-wife-my-wife-is-dead/ |website=Letters of Note |access-date=April 23, 2013 }}</ref> Unable to focus on research problems, Feynman began tackling physics problems, not for utility, but for self-satisfaction.{{sfn|Mehra|1994|pp=171–174}} One of these involved analyzing the physics of a twirling, [[Nutation|nutating]] disk as it is moving through the air, inspired by an incident in the cafeteria at Cornell when someone tossed a dinner plate in the air.{{sfn|Gleick|1992|pp=227–229}} He read the work of Sir [[William Rowan Hamilton]] on [[quaternions]], and tried unsuccessfully to use them to formulate a [[special relativity|relativistic]] theory of electrons. His work during this period, which used equations of rotation to express various spinning speeds, ultimately proved important to his Nobel Prize–winning work, yet because he felt burned out and had turned his attention to less immediately practical problems, he was surprised by the offers of professorships from other renowned universities, including the [[Institute for Advanced Study]], the [[University of California, Los Angeles]], and the [[University of California, Berkeley]].{{sfn|Mehra|1994|pp=171–174}}

[[File:Feynman EP Annihilation.svg|thumb|left|alt=A diagram displaying two particles colliding and releasing gamma radiation|Feynman diagram of electron/positron annihilation]]
Feynman was not the only frustrated theoretical physicist in the early post-war years. [[Quantum electrodynamics]] suffered from [[infinity|infinite]] integrals in [[perturbation theory]]. These were clear mathematical flaws in the theory, which Feynman and Wheeler had tried, unsuccessfully, to work around.{{sfn|Mehra|1994|pp=213–214}} "Theoreticians", noted [[Murray Gell-Mann]], "were in disgrace".{{sfn|Gleick|1992|p=232}} In June 1947, leading American physicists met at the [[Shelter Island Conference]]. For Feynman, it was his "first big conference with big men&nbsp;... I had never gone to one like this one in peacetime."{{sfn|Mehra|1994|p=217}} The problems plaguing quantum electrodynamics were discussed, but the theoreticians were completely overshadowed by the achievements of the experimentalists, who reported the discovery of the [[Lamb shift]], the measurement of the [[magnetic moment]] of the electron, and [[Robert Marshak]]'s [[pi-meson|two-meson]] hypothesis.{{sfn|Mehra|1994|pp=218–219}}

Bethe took the lead from the work of [[Hans Kramers]], and derived a [[renormalization|renormalized]] non-relativistic quantum equation for the Lamb shift. The next step was to create a relativistic version. Feynman thought that he could do this, but when he went back to Bethe with his solution, it did not converge.{{sfn|Mehra|1994|pp=223–228}} Feynman carefully worked through the problem again, applying the path integral formulation that he had used in his thesis. Like Bethe, he made the integral finite by applying a cut-off term. The result corresponded to Bethe's version.{{sfn|Mehra|1994|pp=229–234}}<ref>{{cite web |last=Feynman |first=Richard P. |date=December 11, 1965 |title=Richard P. Feynman – Nobel Lecture: The Development of the Space–Time View of Quantum Electrodynamics |url=https://www.nobelprize.org/prizes/physics/1965/feynman/lecture/ |access-date=June 10, 2023 |publisher=Nobel Foundation}}</ref> Feynman presented his work to his peers at the [[Pocono Conference]] in 1948. It did not go well. [[Julian Schwinger]] gave a long presentation of his work in quantum electrodynamics, and Feynman then offered his version, entitled "Alternative Formulation of Quantum Electrodynamics". The unfamiliar [[Feynman diagrams]], used for the first time, puzzled the audience. Feynman failed to get his point across, and [[Paul Dirac]], [[Edward Teller]] and Niels Bohr all raised objections.{{sfn|Mehra|1994|pp=246–248}}{{sfn|Gleick|1992|pp=256–258}}

To [[Freeman Dyson]], one thing at least was clear: [[Shin'ichirō Tomonaga]], Schwinger and Feynman understood what they were talking about even if no one else did, but had not published anything. He was convinced that Feynman's formulation was easier to understand, and ultimately managed to convince Oppenheimer that this was the case.{{sfn|Gleick|1992|pp=267–269}} Dyson published a paper in 1949, which added new rules to Feynman's that told how to implement renormalization.<ref>{{cite journal|first=F. J. |last=Dyson |author-link=Freeman Dyson |title= The radiation theories of Tomonaga, Schwinger, and Feynman |journal=Physical Review |volume=75|pages=486–502|year=1949|doi=10.1103/PhysRev.75.486|issue=3|bibcode = 1949PhRv...75..486D |doi-access=free}}</ref> Feynman was prompted to publish his ideas in the ''Physical Review'' in a series of papers over three years.{{sfn|Gleick|1992|pp=271–272}} His 1948 papers on "A Relativistic Cut-Off for Classical Electrodynamics" attempted to explain what he had been unable to get across at Pocono.{{sfn|Mehra|1994|pp=251–252}} His 1949 paper on "The Theory of Positrons" addressed the [[Schrödinger equation]] and [[Dirac equation]], and introduced what is now called the [[Feynman propagator]].{{sfn|Mehra|1994|pp=271–272}} Finally, in papers on the "Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction" in 1950 and "An Operator Calculus Having Applications in Quantum Electrodynamics" in 1951, he developed the mathematical basis of his ideas, derived familiar formulae and advanced new ones.{{sfn|Mehra|1994|pp=301–302}}

While papers by others initially cited Schwinger, papers citing Feynman and employing Feynman diagrams appeared in 1950, and soon became prevalent.{{sfn|Gleick|1992|pp=275–276}} Students learned and used the powerful new tool that Feynman had created. Computer programs were later written to evaluate Feynman diagrams, enabling physicists to use quantum field theory to make [[Precision tests of QED|high-precision predictions]].<ref>{{Cite journal |last1=Aoyama |first1=Tatsumi |last2=Kinoshita |first2=Toichiro |last3=Nio |first3=Makiko |date=February 8, 2018 |title=Revised and improved value of the QED tenth-order electron anomalous magnetic moment |url=https://link.aps.org/doi/10.1103/PhysRevD.97.036001 |journal=Physical Review D |language=en |volume=97 |issue=3 |pages=036001 |doi=10.1103/PhysRevD.97.036001 |arxiv=1712.06060 |bibcode=2018PhRvD..97c6001A |s2cid=118922814 |issn=2470-0010}}</ref> [[Marc Kac]] adapted Feynman's technique of summing over possible histories of a particle to the study of [[parabolic partial differential equation]]s, yielding what is now known as the [[Feynman–Kac formula]], the use of which extends beyond physics to many applications of [[stochastic processes]].<ref>{{cite journal|last=Kac|first=Mark|title=On Distributions of Certain Wiener Functionals|journal=Transactions of the American Mathematical Society|author-link=Mark Kac|volume=65|issue=1|pages=1–13|jstor=1990512|year=1949|doi=10.2307/1990512|doi-access=free}}</ref> To Schwinger, however, the Feynman diagram was "pedagogy, not physics".{{sfn|Gleick|1992|p=276}}

Looking back on this period, Feynman would reflect fondly on his time at the [[Telluride House]], where he resided for a large period of his Cornell career. In an interview, he described the House as "a group of boys that have been specially selected because of their scholarship, because of their cleverness or whatever it is, to be given free board and lodging and so on, because of their brains". He enjoyed the house's convenience and said that "it's there that I did the fundamental work" for which he won the Nobel Prize.<ref>{{cite interview |last1=Feynman |first1=Richard |interviewer=Charles Weiner |title=Richard Feynman – Session III |url=https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-3 |access-date=June 19, 2016 |archive-url=https://web.archive.org/web/20160809045333/https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-3 |archive-date=August 9, 2016 |url-status=live |publisher=American Institute of Physics |date=March 5, 1966}}</ref>{{sfn|Feynman|1985|p=191}} 

However, Feynman was also reported to have been quite restless during his time at Cornell. By 1949, as the period was coming to a close, he had never settled into a particular house or apartment, moving instead between guest houses or student residences. While he did spend some time living with various married friends, these situations were reported to frequently end because the "arrangements became sexually volatile".{{sfn|Gleick|1992|p=277}} The renowned 31 year old was known to frequently pursue his married female friends, undergraduate girls and women, and to hire sex workers, which would sour many of his friendships.{{sfn|Gleick|1992|p=287}} Additionally, Feynman was not fond of Ithaca's cold winter weather or feeling as though he lived in the shadow of Hans Bethe while at Cornell.{{sfn|Feynman|1985|pp=232–233}}