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Feynman's thesis [electronic resource] : a new approach to quantum theory

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• # Least Action in Classical Mechanics: # The Concept of Functional # The Principle of Least Action # Conservation of Energy. Constants of the Motion # Particles Interacting Through an Intermediate Oscillator # Least Action in Quantum Mechanics: # The Lagrangian in Quantum Mechanics # The Calculation of Matrix Elements in the Language of a Lagrangian # The Equations of Motion in Lagrangian Form # Translation to the Ordinary Notation of Quantum Mechanics # The Generalization to Any Action Function # Conservation of Energy. Constants of the Motion # The Role of the Wave Function # Transition Probabilities # Expectation Values for Observables # Application to the Forced Harmonic Oscillator # Particles Interacting Through an Intermediate Oscillator # Space-Time Approach to Non-Relativistic Quantum Mechanics # The Lagrangian in Quantum Mechanics.
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Richard P. Feynman Papers

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This collection documents the career of Nobel Prize winner Richard Phillips Feynman (1918-1988). It contains correspondence, biographical materials, course and lecture notes, speeches, manuscripts, publications, and technical notes relating to his work in quantum electrodynamics. Feynman served as Richard Chace Tolman Professor of Theoretical Physics at the California Institute of Technology from 1951 until his death.

• Creation: 1933-1988
• Feynman, Richard P. (Richard Phillips), 1918-1988 (Person)

Conditions Governing Access

This collection has not been digitized, and is available only in the reading room of the Caltech Archives. Access is available to anyone conducting research for which it is necessary; please contact the Caltech Archives to make an appointment.

Conditions Governing Use

Copyright to this collection is not held by Caltech. If you wish to quote or reproduce an item created by Richard Feynman beyond the extent of fair use, please contact his heirs' agent, Melanie Jackson Agency, at [email protected]. Copyright to works by others may be held by their respective creators or publishers, or their heirs. If you wish to quote or reproduce them beyond fair use, please contact the copyright holder to request permission. ("Fair use" is a legal principle which permits unlicensed reproduction in certain circumstances. You are responsible for determining whether your own reproduction would fit the legal requirements for fair use.)

Biographical / Historical

Physicist Richard Feynman won his scientific renown through the development of quantum electrodynamics, or QED, a theory describing the interaction of particles and atoms in radiation fields. As a part of this work he invented what came to be known as "Feynman Diagrams," visual representations of space-time particle interactions. For this work he was awarded the Nobel Prize in physics, together with J. Schwinger and S. I. Tomonaga, in 1965. Later in his life Feynman became a prominent public figure through his association with the investigation of the space shuttle Challenger explosion and the publication of two best-selling books of personal recollections. Feynman was born in the borough of Queens in New York City on May 11, 1918. He grew up and attended high school in Far Rockaway, New York. In 1939, he received his BS degree in physics from the Massachusetts Institute of Technology. He then attended Princeton University as a Proctor Fellow from 1940 to 1942, where he began his investigation of quantum electrodynamics under the supervision of J. A. Wheeler. He was awarded his PhD in 1942 for his thesis on the least action principle. While still at Princeton, Feynman was recruited for the atomic bomb project. He was transferred to Los Alamos in 1942, where he headed a team undertaking complicated calculations using very primitive computers. While at Los Alamos, Feynman became good friends with Hans Bethe, who at the end of the war secured a position for Feynman as an associate professor of physics at Cornell. Feynman remained at Cornell from 1945 to 1951. During this time he formalized his theory of quantum electrodynamics and began to publish his results. He also participated in the Shelter Island Conference of 1947, which helped to determine the course of American physics in the atomic age. At this conference he introduced his theory of QED to the leading American physicists. In 1951, Feynman accepted an offer to become the Richard Chace Tolman Professor of Theoretical Physics at the California Institute of Technology, a position he filled until his death. While at Caltech Feynman continued his work at the leading edge of theoretical physics, making important contributions to the study of liquid helium, particle physics, and later quantum chromodynamics. He also began his distinguished career as a teacher and lecturer. In 1961 and 1962 he delivered to Caltech's freshmen the introductory lectures that were later published as The Feynman Lectures on Physics . In 1986, Feynman was asked to serve on the Presidential Commission investigating the space shuttle Challenger accident. In a dramatic fashion, Feynman publicly demonstrated the inelasticity of the shuttle's O-rings at near freezing temperatures, a leading cause of the disaster. He also contributed an extended appendix to the Committee's report, highlighting the technical and administrative deficiencies of the National Aeronautics and Space Administration's space program. Feynman's many interests outside of science, such as his fondness for codes and safecracking, his bongo drums, his theatrical appearances, his artwork, plus his experiments in out-of-body experiences, are well documented in his autobiographies, as well as in his papers at Caltech. Feynman continued his scientific work and his lecturing activities up until his death on February 15, 1988, after a long battle with a rare form of cancer.

39 linear feet (93 boxes)

Language of Materials

Additional description, arrangement.

The two groups of papers have been kept separate, although box numbering is continuous throughout the collection. The guide to the collection is in two parts, and researchers must expect to consult both parts. At the time the second group of papers was processed, an effort was made to create an arrangement parallel to that of group 1. However, the different content and larger scope of group 2 eventually resulted in a somewhat different scheme. Correspondence: The Feynman collection contains a large amount of both incoming and outgoing correspondence. Feynman's scientific contacts include many of the greatest names in twentieth-century physics: Hans Bethe, Niels Bohr, Enrico Fermi, Stephen Hawking, Werner Heisenberg, J. Robert Oppenheimer, Hideki Yukawa—to name only a few. In Group 1, correspondence has been spread over four series: correspondence (largely with individual colleagues), miscellaneous or general correspondence, publication correspondence, and, in the biographical series, a small number of personal letters. For Group 2, an attempt was made to pull both personal, general, and publication correspondence into one main series, Series 1. However, when letters demonstrated both intellectual and physical links with other documents, their original contextual relationships were maintained. Thus, publication correspondence will be found both in Series 1 and in Series 6. Fan mail surrounding Feynman's television appearances, his two autobiographies, and his Nobel Prize has been placed in Series 2, Biographical, as has other correspondence relating to his business and consulting activities documented there. Course and Lecture Notes: Feynman's lecture courses at institutions in Southern California other than Caltech, and even outside the U.S., are represented in Group 2. Of special interest are the courses Feynman gave, in addition to those he attended, at Hughes Aircraft Company, and the sets of lectures that were later published as Statistical Mechanics and QED (originally the Mautner Lectures, which were in turn predated by the Robb Lectures, first delivered at the University of Aukland, New Zealand). Material pertaining to the publication of these lecture series is found in Group 2 correspondence under the respective publishers. Talks, Speeches, Conferences: In this category are those lectures delivered for a special occasion or purpose, usually as single lectures, but sometimes as a series, and in both formal and informal settings. This category overlaps somewhat with Course Notes and Lectures. In Group 1, these materials are to be found under Professional Organizations and Meetings (Series 3) and Manuscripts (Series 5). In Group 2, they are arranged under Series 5 in chronological order, when dated, and in a sub-series of undated talks. Folders in this category contain a wide variety of talk-related documents, from holograph notes to correspondence to slides, figures, or transparencies. Publications: Group 1 contains a small series of publication correspondence (Group 1, Series 4), mostly pertaining to Feynman's book or monograph publishers; in Group 2, similar correspondence has been placed in the main correspondence series (Group 2, Series 1). Group 2's Series 6 lists Feynman's publications by title in chronological order. Folders contain a variety of material, from holograph notes to correspondence to proofs and prints. Researchers should note that formal reprints have been grouped at the end of Group 2, in Section 9. Working Notes and Calculations: The vast majority of Feynman's working notes are located in Group 2. A representative sample from his early years appears in Group 1, Series 5. Of special interest in this group are notebooks from his student days, beginning circa 1933. The notes in Group 2 capture the breadth and depth of Feynman's thought, as well as reflecting many aspects of his personality. They cover a wide range of subjects, from quantum electrodynamics and later quantum chromodynamics to biology and computers. The notes also reflect Feynman's working style. They are sometimes carefully organized into notebooks that were rigorously dated, such as the binders dated between 1966 and 1987 at the beginning of Group 2, Series 7. Unfortunately for researchers, these are the exception. The great mass of Feynman's working notes are scattered on miscellaneous sheets of papers, envelopes, placemats, and seemingly whatever else was at hand when thoughts struck him. Feynman occasionally took time to organize these into a system for files, although only a small fraction of his notes found their way into such a system. The great majority was left in a scattered condition and grouped during the processing of the papers as well as possible by subject matter. Many miscellaneous papers remain. Work of Others: Feynman officially maintained neutrality on the work of his contemporaries, but informal commentaries in the form of notes and marginal glosses on the work of others abound in his papers. A small segment of such materials can be found in Group 1, Series 5. A large amount of work by others, both with and without Feynman's commentary, forms Group 2's Series 8. A preponderance of material on computers dictated an arrangement in which computer-related projects are categorized separately. Individuals whose work is strongly represented—largely Caltech colleagues, students, or collaborators—are listed singly; otherwise materials have been listed by subject.

Immediate Source of Acquisition

The Richard Phillips Feynman Papers were given to Caltech by Richard Feynman and Gweneth Feynman in two main installments. The first group of papers, now boxes 1-20 of the collection, was donated by Richard Feynman himself beginning in 1968, with additions later. It contains materials dating from about 1933 to 1970. The second group occupies boxes 21-90. It was given to Caltech by Feynman's widow Gweneth early in 1989. Group 2 contains papers primarily from the 1970s and 1980s, although some older material is present. Supplements since 1994 occupy three boxes and have come from various donors outside the Feynman family.

Related Materials

Researchers should also consult the Caltech Archives' Historical Files, which contain much miscellaneous material on Richard Feynman acquired from many sources. Similarly the Photo Archives offer a selection of images, obtained in a similar way. The audio and video collections contain substantial Feynman material; researchers should consult the specific index. Manuscript collections at Caltech which contain materials of particular relevance to Feynman include the Robert Leighton Papers and course lecture notes by Bruce H. Morgan.

Processing Information

The initial processing of this collection was completed on July 1, 1993.

• Challenger (Space shuttle)
• Gravitation--Research
• Particles (Nuclear physics)
• Physics--Study and teaching
• Quantum chromodynamics
• Quantum electrodynamics
• Quantum theory
• Space shuttles--Accidents--Investigation--United States

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Part of the California Institute of Technology Archives and Special Collections Repository

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Richard P. Feynman Papers, FeynmanRP2. California Institute of Technology Archives and Special Collections.

Cite Item Description

Richard P. Feynman Papers, FeynmanRP2. California Institute of Technology Archives and Special Collections. https://collections.archives.caltech.edu/repositories/2/resources/168 Accessed May 14, 2024.

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Feynman's Thesis: A New Approach to Quantum Theory

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Richard Feynman

Notable works: selected scientific works.

Feynman, Richard P. (2000). Laurie M. Brown, ed. Selected Papers of Richard Feynman: With Commentary. 20th Century Physics. World Scientific.

Feynman, Richard P. (1942). Laurie M. Brown, ed. The Principle of Least Action in Quantum Mechanics. Ph.D. Dissertation, Princeton University. World Scientific (with title Feynman's Thesis: a New Approach to Quantum Theory) (published 2005).

Wheeler, John A.; Feynman, Richard P. (1945). "Interaction with the Absorber as the Mechanism of Radiation". Rev. Mod. Phys. 17 (2–3): 157–181.

Feynman, Richard P. (1946). A Theorem and its Application to Finite Tampers. Los Alamos Scientific Laboratory, Atomic Energy Commission.

Feynman, Richard P.; Welton, T. A. (1946). Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials. Los Alamos Scientific Laboratory, Atomic Energy Commission.

Feynman, Richard P.; Metropolis, N.; Teller, E. (1947). Equations of State of Elements Based on the Generalized Fermi-Thomas Theory. Los Alamos Scientific Laboratory, Atomic Energy Commission.

Feynman, Richard P. (1948a). "Space-time approach to non-relativistic quantum mechanics". Rev. Mod. Phys. 20 (2): 367–387.

Feynman, Richard P. (1948b). "Relativistic Cut-Off for Quantum Electrodynamics". Physical Review 74 (10): 1430–1438.

Wheeler, John A.; Feynman, Richard P. (1949). "Classical Electrodynamics in Terms of Direct Interparticle Action". Rev. Mod. Phys. 21 (3): 425–433.

Feynman, Richard P. (1949). "The theory of positrons". Phys. Rev. 76 (6): 749–759.

Feynman, Richard P. (1949b). "Space-Time Approach to Quantum Electrodynamic". Phys. Rev. 76 (6): 769–789.

© Estate of Richard Feynman 2021

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• Published: 25 May 2023

In retrospect

75 years of the path integral formulation

• Alison Wright 1  

Nature Reviews Physics volume  5 ,  page 321 ( 2023 ) Cite this article

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In what has to be one of the clearest abstracts ever written, Richard Feynman put it simply thus: “Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation.”

The abstract goes on: “The probability that a particle will be found to have a path x ( t ) lying somewhere within a region of space time is the square of the sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ħ ) for the path in question.” Feynman was moving away from the idea of a single, classical trajectory for a system, and instead thinking quantum mechanically about all possible trajectories, summing over all possible paths — the path integral formulation. Then, he concludes, “The total contribution from all paths reaching x , t from the past is the wave function Ψ ( x , t ). This is shown to satisfy Schrödinger’s equation.”

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Original article

Feynman, R. P. Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20 , 367–387 (1948)

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Dyson, F. J. The radiation theories of Tomonaga, Schwinger, and Feynman. Phys. Rev. 75 , 486–502 (1949)

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Wright, A. 75 years of the path integral formulation. Nat Rev Phys 5 , 321 (2023). https://doi.org/10.1038/s42254-023-00601-3

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Published : 25 May 2023

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DOI : https://doi.org/10.1038/s42254-023-00601-3

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The doctoral students of Richard Feynman

Contrary to conventional wisdom, the legendary physicist supervised more than 30 doctoral students, many of whom have become prominent in their fields.

“An ordinary genius is an ordinary fellow . . . There is no mystery as to how his mind works . . . It is different with the magicians . . . Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students . . . Richard Feynman is a magician of the highest caliber.” —Mark Kac, Enigmas of Chance

As the centennial of Richard Feynman’s birth approaches, it’s a good time to dispel a minor myth about him: that he had very few doctoral students. The myth is embodied in the words of Mark Kac above and in a statement attributed to one of his students, Philip Platzman: “The reason why Feynman did not have many students was because he was very difficult with them, because he didn’t really worry about students . . . He had a few students, but not many.” Despite such statements, which seem to represent the prevailing belief in the scientific community, the claim that Feynman did not often supervise students for their PhD theses is simply not true.

The number of Feynman’s doctoral students is actually about 30, with some uncertainty due to unavailable documents as well as possible subjectivity on my part. The lineup of students who completed their PhD research under Feynman’s discerning gaze begins with Michel Baranger, Laurie Brown, and Giovanni Lomanitz at Cornell University in 1951 and concludes with Ted Barnes and Thomas Curtright at Caltech in 1977.

Although 30 is not an extremely large number of doctoral students to have mentored during a lifetime as an academic (Julian Schwinger, for example, supervised at least 70 during five decades), it does amount to three PhDs for every four years of Feynman’s time as a professor. If not for illness during the last several years of his career, Feynman might have supervised several more students.

The most recognized physicist among Feynman’s doctoral students is undoubtedly George Zweig, who graduated from Caltech in 1964. Soon thereafter Zweig had a major impact on elementary-particle physics through his independent invention of the quark model of hadrons. The research of Feynman’s other students has also had significant impact and continues to influence several areas of physics.

At the time of this writing, Wikipedia lists only six students to have officially received PhDs with Feynman as the adviser. The mother lode of information about Feynman’s doctoral students can be found at the Caltech library. A direct search of the school’s online database produces a list of 25 PhD theses in which Feynman is described as the adviser or co-adviser. By way of comparison, a direct search for his Caltech colleague Murray Gell-Mann as adviser turns up 16 theses. Zweig, along with Henry Hilton and Michael Levine, were co-advised by Feynman and Gell-Mann. Beyond publicly accessible sources, the largest amount of documentation on Feynman’s doctoral students came from Curtright.

From looking at many theses and papers by Caltech students, my overall impression is that Feynman played a major role in the school’s graduate program in physics through his mentoring and supervision of doctoral students. He exerted tremendous influence on graduate student research conducted at Caltech during his four decades there—perhaps even more than his widely perceived influence on Caltech undergraduate studies.

The Students

“There are PhDs, and then there are Feynman PhDs.” —Richard Sherman

From theses and PhD dissertation examination documents in which it was either explicitly stated or otherwise clear that Feynman was the adviser or co-adviser, I find the 30 doctoral students listed here, the first three at Cornell, the others at Caltech:

• Michel Baranger (1951) “Relativistic corrections to the Lamb shift”
• Laurie Brown (1951) “Radiative corrections to the Klein–Nishina formula”
• Giovanni Lomanitz (1951) “Second order effects in the electron–electron interaction”
• Albert Hibbs (1955) “The growth of water waves due to the action of the wind”
• William Karzas (1955) “The effects of atomic electrons on nuclear radiation”
• Koichi Mano (1955) “The self-energy of the scalar nucleon”
• Gerald Speisman (1955) “The neutron–proton mass difference”
• Truman Woodruff (1955) “On the orthogonalized plane wave method for calculating energy Eigen-values in a periodic potential”
• Michael Cohen (1956) “The energy spectrum of the excitations in liquid helium”
• Samuel Berman (1959) “Radiative corrections to muon and neutron decay”
• Frank Vernon (1959) “The theory of a general quantum system interacting with a linear dissipative system”
• Willard Wells (1959) “Quantum theory of coupled systems having application to masers”
• Henry Hilton (1960) “Comparison of the beta-spectra of boron 12 and nitrogen 12”
• Carl Iddings (1960) “Nuclear size corrections to the hyperfine structure of hydrogen”
• Philip Platzman (1960) “Meson theoretical origins of the non-static two nucleon potential”
• Marvin Chester (1961) “Some experimental and theoretical observations on a configurational EMF”
• Elisha Huggins (1962) “Quantum mechanics of the interaction of gravity with electrons: theory of a spin-two field coupled to energy”
• Harold Yura (1962) “The quantum electrodynamics of a medium”
• Michael Levine (1963) “Neutrino processes of significance in stars”
• George Zweig (1964) “Two topics in elementary particle physics: The reaction [photon-neutron going to pion-nucleon] at high energies. K leptonic decay and partially conserved currents”
• James Bardeen (1965) “Stability and dynamics of spherically symmetric masses in general relativity”
• Howard Kabakow (1969) “A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)”
• Robert Carlitz (1971) “Elimination of parity doubled states from Regge amplitudes”
• Mark Kislinger (1970) “Elimination of parity doublets in Regge amplitudes”
• Finn Ravndal (1971) “A relativistic quark model with harmonic dynamics”
• Richard Sherman (1971) “Surface impedance theory for superconductors in large static magnetic fields”
• Arturo Cisneros (1973) “I. Baryon-antibaryon phase transition at high temperature. II. Inclusive virtual photon-hadron reactions in the parton model”
• Steven Kauffmann (1973) “Ortho-positronium annihilation: steps toward computing the first order radiative corrections”
• Frank (Ted) Barnes (1977) “Quarks, gluons, bags, and hadrons”
• Thomas Curtright (1977) “Stability and supersymmetry”

From documents in which Feynman was not described as an adviser or co-adviser but was a member of the PhD examination committee (although not the committee chairman) and/or was acknowledged in the thesis for moderate influence and general advice, I find in addition:

• Fredrik Zachariasen (1956) “Photodisintegration of the deuteron”
• Paul Craig (1959) “Observations of perfect potential flow and critical velocities in superfluid helium II”
• James Mercereau (1959) “Diffraction of thermal waves in liquid helium II”
• Kenneth Wilson (1961) “An investigation of the Low equation and the Chew–Mandelstam equations”
• John Andelin (1966) “Superfluid drag in helium II”
• Karvel Thornber (1966) “I. Electronic processes in α-sulfur. II. Polaron motion in a D.C. electric field”
• Lorin Vant-Hull (1967) “Verification of long range quantum phase coherence in superconducting tin utilizing electromagnetically stabilized Josephson junctions”
• William Press (1973) “Applications of black-hole perturbation techniques”
• Robert Wang (1976) “A study of some two-dimensional field theory models”
• Don Page (1976) “Accretion into and emission from black holes”
• Stephen Wolfram (1980) “Some topics in theoretical high-energy physics”

I also find several less compelling cases where Feynman was only a member of the dissertation examination committee at Caltech and was not particularly influential in the research, as far as I can tell. I suspect there are many more such cases that I have not found, since on this point documentation is quite often incomplete and not all committee members are listed. For example:

• Richard Lipes (1969) “I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering”
• Christopher Hill (1977) “Higgs scalars and the nonleptonic weak interactions”
• William Dally (1986) “A VLSI architecture for concurrent data structures”
• John Wawrzynek (1987) “VLSI concurrent computation for music synthesis”

T. S. Van Kortryk is an amateur mathematician based in Paris, Missouri, who has an interest in the history of physics.

Editor’s note, 30 August: Due to a change in the thesis information provided by Caltech and further research, the author has determined that Feynman did not serve as co-adviser for Sandip Trivedi’s 1990 thesis. Two references to that thesis were removed from the article, and the minimum number of Feynman doctoral students was revised from 31 to 30.

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