Selected Papers of Richard Feynman

The following sections are included:

• CONTENTS

• PREFACE

• RICHARD PHILLIPS FEYNMAN

In his final year as an undergraduate at the Massachusetts Institute of Technology, Feynman published with one of his teachers, Manuel S. Vallarta, a Letter to the Editor of the Physical Review on cosmic rays [1]. He also completed a senior dissertation under John C. Slater entitled “Forces and Stresses in Molecules” and published a shortened version, “Forces in Molecules,” as an article in the Physical Review. The latter contained a result — a general quantum-mechanical theorem — that has played an important role in theoretical chemistry and condensed matter physics and is frequently cited as the Hellmann–Feynman theorem.¹ According to Feynman's abstract, “The force on a nucleus in an atomic system is shown to be just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution.” Quantum mechanics is used to calculate the charge distribution as the absolute square of the Schrödinger wave function. The importance of the forces on the atomic nuclei for molecular geometry, the theory of chemical binding, and for crystal structure is evident…

While Feynman made many original and imaginative contributions to theoretical physics, it may well be that his place in the history of science will be largely based on his approach to renormalizing quantum electrodynamics (QED), and especially on the tools that he invented to accomplish that goal, such as path integrals, the operator calculus, and the famous Feynman diagrams. Eventually QED may be replaced by a finite theory, rather than the present divergent, though renormalizable, one. (QED is already incorporated in the unified electroweak theory, one of the two parts of the Standard Model.) Feynman himself never regarded renormalized QED as complete, frequently pointing out its limitations and suggesting that it was merely what we now call an “effective field theory.” But even if QED proves to be transitory, the theoretical methods that Feynman developed are permanently embedded in mathematical physics, and have been widely applied in areas far beyond their original domain…

The Feynman path integral approach to quantum mechanics stands presently on a par, both esthetically and practically, with the original formulations of 1925–26.¹ The path integral formulation of the quantum gauge theories which lie at the heart of the Standard Model of elementary particle interactions turned out to be critical in the Veltman–'t Hooft proof that these theories are renormalizable. However, it has an even wider range of applications than to quantum field theories. Feynman's book of 1965 with Albert R. Hibbs [64] uses path integrals to treat problems other than quantum mechanics and quantum electrodynamics, including statistical mechanics, the variational principle, the polaron problem, Brownian motion, and noise. Other applications have been made to quantum liquids and solids, to macromolecules and polymers, and to problems of propagation in dissipative media. The approach is important to various forms of semiclassical approximations in chemical, atomic, and nuclear problems and basic to the instanton problem (barrier penetration between different vacuum ground states). It can be extended to optics and even to the motion of particles in the strong gravitational fields near a black hole…

Between 1953 and 1958, Feynman published a seminal series of papers on the atomic theory of superfluid helium. Superfluidity in liquid helium had been discovered in the 1930's, and the early understanding of this phenomenon relied on Landau's phenomenological theory (1941, 1947) of phonons and rotons as elementary excitations (“quasiparticles”). In this context, the Bose–Einstein statistics of helium atoms (and the existence of a Bose–Einstein condensate) played essentially no role. [For a summary of the early history see, for example, A. Griffin, in Bose–Einstein Condensation in Atomic Gases, edited by M. Inguscio, S. Stringari, and C.E. Wieman (Italian Physical Society, 1999).] A significant part of Feynman's central contribution was the demonstration that these phenomenological concepts arose directly from the fundamental quantum mechanics of interacting bosonic atoms with strong repulsive cores…

Throughout his career, Feynman worked mainly in the area of physics denoted as “particles and fields,” and while his interests also roamed into wider pastures, his home base remained the study of the strong, electromagnetic and weak interactions of the so-called elementary particles. Thus it was inevitable that he would become a major player in the development of high energy physics, trying to explain the important experimental discoveries in cosmic rays of the decade following World War II, and continuing with the “particle explosion” resulting from the use of the great accelerators and detectors as they came on-line in the subsequent decades…

Feynman worked seriously on the quantum theory of gravity for about a decade, beginning in the early 1950s.¹ In the introduction to paper [57] he wrote that his interest was “primarily in the relation of one part of nature to another,” rather than in explaining phenomena or fitting data. In working out (absurdly small) one-loop quantum radiative corrections, he hoped that he would not be criticized “for the fact that there is no possible, practical reason for making these calculations.”…

Feynman's interest in numerical computation dated back to his wartime Los Alamos days, when Bethe put him in charge of a group doing calculations to model the plutonium implosion bomb. Feynman developed a system, using persons at mechanical calculators in a system analogous to what would much later, with digital computers, be called “parallel computing.” During the last ten years of his life he became fascinated by the theory and application of computers and he gave a joint course in computation at Caltech, together with his colleagues John Hopfield and Carver Mead, also using guest lecturers.¹ Feynman also published three papers on computers. (Papers [110] and [115] are the same.)…

The following sections are included:

• BIBLIOGRAPHY