# Schwinger, Julian Seymour

# SCHWINGER, JULIAN SEYMOUR

(*b*. New York, New York, 12 February 1918; *d*. Los Angeles, California, 16 July 1994),

*electromagnetic theory, quantum mechanics, atomic physics, nuclear theory, quantum field theory, high energy and elementary particle physics*.

On 13 June 1978 the Nobel laureate Chen Ning Yang wrote the following to the chairman of the physics department at the University of California, Los Angeles (UCLA) to support Julian Schwinger’s appointment as professor:

Professor Julian Schwinger is among the great physicists of the contemporary era. His work covers an amazing range, from nuclear physics to elementary particle physics to field theory, from synchrotron radiation to group theory to microwave propagation.… The most important work of Schwinger was his contribution to renormalization, a contribution that stands among the greatest developments in physics in mid-twentieth century. Professor Schwinger is an eminently successful teacher. He probably has graduated more influential theoretical PhD students than any other living physicist.

**Early Years** Julian Schwinger was born into a middle-class Jewish family. Schwinger’s mother, Belle Rosenfeld, was born in Lodz, a large manufacturing town in eastern Poland, which was then a part of Russia. Her family had emigrated to the United States when she was a very young child. Benjamin Schwinger, Julian’s father, was born in Newsandez, a small village in the foothills of the Carpathian Mountains in one of the provinces of the Austrio-Hungarian Empire. He came to the United States around 1880 and eventually became a successful designer of women’s clothing.

After they were married, Schwinger’s parents lived near Morris Park in Harlem, then a well-to-do Jewish neighborhood. Their first son, Harold, was born in 1911. Some six years later they moved to a large apartment at 640 Riverside Drive near 141st Street. Julian Seymour was born on 12 February 1918. Benjamin Schwinger was a talented couturier, and his business had prospered. Like his elder brother, Julian Schwinger attended Townsend Harris High School, then one of the best secondary

** Julian Schwinger** .

*Schwinger diagramming on a blackboard*.

**SPL/PHOTO RESEARCHERS, INC**.

schools in the United States. He graduated in 1934, and entered City College of New York (CCNY) in the fall of that year as a physics major. His precocity and ability in physics were legendary even during his high school years. As a freshman at CCNY, Schwinger had regularly attended the weekly theoretical seminar that Isidor Rabi, Gregory Breit, and Otto Halpern ran at Columbia University on Wednesday evenings. The sixteen-year-old undergraduate clearly must have impressed Halpern, for in 1935 they published a joint paper on the problem of the polarization of electrons in double scattering experiments, the young Julian having done extensive and difficult calculations.

Schwinger, nevertheless, did not do well at CCNY. He spent most of his time in the library, reading advanced physics and mathematical texts, and rarely went to his classes. His grades reflected his erratic attendance. Although he had no difficulty getting As in mathematics and physics courses (even though he rarely attended), the same was not the case in his other courses. The matter became serious enough for Lloyd Motz, one of his physics instructors at CCNY who was studying for his PhD at Columbia University, to bring Schwinger’s problems to the attention of Rabi. Rabi was influential in obtaining a scholarship for Schwinger to come to Columbia. He did well there, though some of the previous problems remained. During his senior year, Schwinger worked on the problem of the magnetic scattering of slow neutrons by atoms. He formulated a fully quantum mechanical treatment of the problem and found that neutrons scattered from an unpolarized beam would be partially polarized by virtue of the magnetic interaction—and that the polarization thus produced could be detected by a second scattering. In early January 1937 Schwinger sent a manuscript describing his research, titled “The Magnetic Scattering of Neutrons,” to the *Physical Review*.

All the characteristics that Schwinger exhibited in his subsequent works were present in this paper: an important physical problem was addressed; the solution was elegant; the methods used were powerful; contact was made with experimental data; and suggestions for empirical tests were given. Edward Teller, who was visiting Columbia during the spring term of 1937, suggested that Schwinger’s research on the scattering of neutrons could be submitted as a PhD thesis if he developed them further. Schwinger worked with Teller and showed that the scattering of neutrons by ortho- and para-hydrogen could yield information about the spin dependence and the range of the neutron-proton interaction. The fact that Schwinger had written his PhD dissertation before receiving his bachelor’s degree is indicative of his remarkable talents.

**Columbia and Berkeley** After receiving his BS from Columbia in 1936, Schwinger continued his graduate studies there. Shortly after becoming a graduate student, Schwinger received a traveling fellowship from Columbia for the academic year 1937–1938. The plans were for him to spend six months at Wisconsin to study with Gregory Breit and Eugene Wigner, and then to go on to the University of California, Berkeley, for another six months to work with J. Robert Oppenheimer. He remained at Wisconsin for the year and there developed his characteristic working habits: staying up at night and sleeping during the day. In private, Schwinger indicated that he started staying up at night because of a strong feeling of not wanting to be “dominated” by Wigner and Breit.

Rabi characterized Schwinger “a changed man” when he returned to Columbia after his year at Wisconsin. He became deeply involved in the experimental activities in Rabi’s laboratory. Even before going to Wisconsin, stimulated by Rabi’s atomic beam experiments, Schwinger had written a paper on the behavior of an arbitrary magnetic moment in a harmonically time-varying magnetic field that has become a classic. This association with Rabi and his atomic beam experiments resulted in Schwinger’s protracted fascination with atomic and nuclear moments, and more generally, with the quantum theory of angular momentum. Schwinger also became the “house theorist” for the experiments in nuclear physics being carried out at Columbia at the time. Schwinger’s papers from that period reflect not only his wide interests—for example, the scattering of neutrons by hydrogen molecules and by deuterons, the quadrupole moment of the deuteron, the effect of tensor forces on the scattering of neutrons by protons, the widths of nuclear energy levels—but also attest to his talents as a superb phenomenologist.

In the fall of 1939 Schwinger went to Berkeley. By his own admission, Oppenheimer’s influence on him was enormous. Oppenheimer steered Schwinger into areas of physics in which he had not yet worked: cosmic rays, meson spin assignments, quantum electrodynamics, and the quantum field theory (QFT) of nuclear forces. Schwinger stayed in Berkeley for two years, the first as a National Research Council Fellow, the second as a research associate to Oppenheimer. His stay was extremely productive. Oppenheimer, as well as the large number of doctoral students and postdoctoral fellows working under his tutelage—Sidney Dancoff, Hartland Snyder, George Volkoff, Leonard Schiff, David Bohm, Philip Morrison, and Robert Serber—made for a very stimulating and congenial atmosphere. Schwinger collaborated extensively— with Bert Corben, Edward Gerjouy, Oppenheimer, and William Rarita—and worked on a wide range of subjects. The investigations ranged from phenomenological analyses of the empirical data on the deuteron and light nuclei to extensive field theoretic calculations using differing spin and charge assignments for the “mesotrons” involved.

A paper by Nicholas Kemmer in 1938 on a meson field theoretical model of the nuclear forces had made Schwinger aware, before his arrival at Berkeley, of the possibility of the presence of tensor forces in the neutron-proton interaction. An analysis of the electromagnetic properties of the deuteron when tensor forces are present led him to predict the existence of the deuteron’s quadrupole moment—before it had been measured by Jerome Kellogg, Norman Ramsey, Rabi, and Jerrold Zacharias in 1939. Tensor forces, and the kind of mesotrons and meson-nucleon couplings that could give rise to them, became a central focus of the investigations Schwinger carried out during the Berkeley period. All his researches from that period have one feature in common: no matter how theoretical or abstract the starting point, whether formulating the QFT of spin 3/2 particles, or investigating the solutions of the Proca equations for a charged spin 1 particle moving in a Coulomb field, contact was always made with “numbers” and with experiments. And in each case Schwinger mastered the intricate details of the experiments that had provided the data he was comparing his numbers to—the apparatus involved as well as the analysis and reduction of the data.

Two pieces of research carried out in Berkeley were later of great importance, when Schwinger worked on quantum electrodynamics in the post–World War II period. The first was a collaboration with Oppenheimer in 1939 that used quantum electrodynamics (QED) to describe electron-positron emission from an excited oxygen nucleus. This calculation brought home to him the physical reality of virtual photon processes. The second was his work on strong-coupling mesotron theory, through which he gained experience in using canonical transformations to extract the physical consequences of a field theory.

**Wartime Research** Schwinger left Berkeley in the summer of 1941 to accept an instructorship at Purdue University. His subsequent contributions to the war effort were determined by his presence at Purdue. An active program in semiconductor research was being carried out there for the Radiation Laboratory (Rad Lab) of the Massachusetts Institute of Technology (MIT) by Karl Lark-Horowitz in order to develop better rectifiers for the detection of radar. In 1942 Schwinger and several other theorists were asked to join a Rad Lab project at Purdue under Hans Bethe’s direction on the propagation of microwave radiation in microwave cavities.

When in early 1943 the Los Alamos Scientific Laboratory was organized to build an atomic bomb, Oppenheimer invited Schwinger to join the laboratory, but he declined. However, because many of the leading theorists at the Rad Lab were leaving it to go to Los Alamos, Schwinger was asked to come to MIT. This he did in the fall of 1943. In his work there, Schwinger solved a wide variety of microwave problems. Using an integral equation formulation of field problems, he introduced and deployed powerful mathematical techniques that became characteristic features of many of his subsequent inquiries: Green’s functions and variational methods. These researches resulted in a rigorous and general theory of microwave structures in which conventional low-frequency electrical theory appeared as a special case. While at the Rad Lab, Schwinger gave lectures on the theory of wave guides that were attended by a small group of colleagues. An abbreviated set of notes—the war ended before the series had finished—were eventually published in 1968 under the title *Discontinuities in Waveguides*, with Schwinger and David Saxon as authors. The lectures exhibited Schwinger’s formidable analytical powers and gave proof of his remarkable ability to be equally at home in the worlds of physics, applied science, engineering, and applied mathematics. In a memorial lecture for Sin-Itiro Tomonaga, delivered in 1980, Schwinger commented that his waveguide investigations showed the utility of organizing a theory to isolate those inner structural aspects that are not probed under the given experimental circumstances. That lesson was subsequently applied to the effective-range description of nuclear forces. And it was this viewpoint that would lead to the quantum electrodynamic concept of self-consistent subtraction or renormalization. While at the Rad Lab, Schwinger also worked on the problem of the radiation emitted by fast electrons traveling in synchrotron orbits. The formulation of this problem taught him the importance of describing relativistic situations covariantly, that is, without specialization to any particular coordinate system.

**Harvard** When in 1944 universities began competing with one another for outstanding figures in physics, Schwinger was courted by a number of them, and in particular by Harvard University. In the fall of 1945 Schwinger accepted an appointment there as an associate professor. A year later he was offered a full professorship at Berkeley, and Harvard promptly promoted him. Harvard provided him with outstanding graduate students, and he became thesis advisor to many of them. They, together with many of MIT’s graduate students and postdoctoral fellows and a fair fraction of the Harvard and MIT physics faculty, formed the audience for Schwinger’s brilliant lectures. The impact and influence of these lectures—and of the widely circulated notes based on them—on the generation of physics graduate students of the late 1940s and 1950s cannot be exaggerated. Many of the later textbooks on nuclear physics, electromagnetic theory, quantum mechanics, QFT, and statistical mechanics incorporated the approaches, techniques, and examples that Schwinger had discussed in his lectures.

**Shelter Island** At a famous meeting held in June 1947 on Shelter Island, at the tip of Long Island, New York, reliable experimental data were presented by Willis Lamb and Robert Retherford that indicated that, contrary to the prediction of the Dirac equation, the 2*S*_{1/2} and 2*P*_{/2} levels of the hydrogen atom were not degenerate, with the 2*S*_{1/2} state lying some 1,000 megahertz above the 2*P*_{/2}. In addition, Rabi reported that he, John E. Nafe, and Edward B. Nelson had made hyperfine measurements in hydrogen and deuterium that indicated that the g value of the magnetic moment of the electron, g (e/2m) 1/2(h/2π) differed from the predicted Dirac value g = 2. Rumors about the Lamb shift had circulated before the meeting. Victor Weisskopf and Schwinger talked about it as they traveled together by train to Shelter Island. Both of them knew that the self-energy of an electron in QED was logarithmically divergent and therefore that if one took the difference of the energies of two fine structure levels, the result would be finite. In fact, Weisskopf had a graduate student, Bruce French, doing such a calculation at MIT. Because he had gotten married to Clarice Carrol shortly after the conference it was only in September 1947 that Schwinger set out on the trail of relativistic QED. He recognized that explaining the anomalous value of the electron’s magnetic moment was the crucial calculation, for it did not involve the complications associated with bound states. Making use of the ideas of mass renormalization—that the (divergent) self-energy, θm, generated by the interaction of the electron-positron field with the (quantized) electromagnetic field must be added to the mass m_{0} attributed to an electron (as specified by the Lagrangian for the electron-positron field) and that the sum m_{0} + δm is to be identified with the experimentally determined mass of the electron—Schwinger obtained in December 1947 the result

g/2 = 1 + α/2π), α = *e/bc h* 1/37

in agreement with the data of Rabi, Nelson, and Nafe. He then proceeded to calculate the Lamb shift, a much more difficult calculation requiring that, in addition to mass renormalization, a charge renormalization be carried out. Charge renormalization reflects the fact that to parameter e_{0} in the Lagrangian that represents the bare charge of an electron must be added the screening effect of virtual pair production in the vacuum (vacuum polarization effects) and that it is their sum that is to be identified with the experimentally determined charge of an electron. Though he obtained a finite answer in close agreement with the Lamb-Retherford value, Schwinger’s calculation was plagued with inconsistencies due to the lack of Lorentz covariance. Schwinger thereafter proceeded to formulate an explicitly covariant approach to QED and to field theory in general. Tomonaga in Japan had developed the same formalism and had written down the same generalization of the Schrödinger equation to an arbitrary space-like surface σ

which equation has become known as the Tomonaga-Schwinger equation. (A spacelike surface is one on which every two points, x, x’ are separated by a spacelike distance, i.e., (x >0.) In (1) *H(* x) is the Hamiltonian density of the field system which for quantum electrodynamics is given by

where j_{μ} (*(x)* is the electric current operator of the electron-positron field and *A ^{μ}(x)* the operator representing the electromagnetic potential.

By the time of the Pocono conference in April 1948, Schwinger had worked out the implications of his new formalism. His covariant formulation, when supplemented with the notions of mass and charge renormalization, was the first self-consistent framework in QFT from which physical consequences could be extracted and checked with experiments. For this work he shared the Nobel Prize in 1965 with Richard Feynman and Tomonaga.

**Quantum Field Theory and Green’s Functions** Schwinger’s covariant approach was communicated to the community at large in a series of papers titled *Quantum Electrodynamics*(Parts I, II, and III) that were submitted to the *Physical Review* in 1948 and 1949. Parts I and II served as the notes for the lectures that Schwinger delivered at the Michigan Summer School in Ann Arbor from 19 July to 7 August 1948. Freeman Dyson, who had just completed a year of graduate studies at Cornell University, was one of the students in Schwinger’s course. During the course of that year he had interacted with Feynman and knew the details of Feynman’s diagrammatic and calculational approach to QED. That fall Dyson proved the equivalence of the two approaches and proceeded to formulate a proof that the S-matrix for QED can be rendered finite to all orders of perturbation theory by mass and charge renormalization. Thereafter Feynman and Dyson’s graphical approach to field theory became the preferred method for the analysis of field theoretic problems, and Schwinger felt that he had to respond.

The challenge for Schwinger became how to formulate local quantum field theories based ab initio on a quantum action principle. He wanted to get away from quantization procedures that were expressed as a set of operator prescriptions imposed on a classical description based upon a Hamiltonian. This approach produced an asymmetry in the treatment of time and space and resulted in a formulation that was noncovariant. Additionally, it placed the existence of anticommuting Fermi-Dirac fields on a purely empirical basis to be introduced into the formalism on an ad hoc basis.

Schwinger’s point of departure were the papers of Feynman in which he had formulated quantum mechanics by exhibiting the probability amplitude connecting the state of a system at one time to that at a later time as a sum of complex unit amplitudes—one for each possible trajectory of the system connecting the initial and final state— the phase of each amplitude being determined by the value of the action, (L dt, for that trajectory. Because action is a relativistic invariant, the formulation could be made covariant. But whereas Feynman gave a global solution, for Schwinger the idea was not, as Feynman had done, to write down the solution, but to continue in the tradition of classical mechanics as a historical model, to find a differential action principle formulation.

In 1951, in eight pages of the *Proceedings of the National Academy of Sciences*, he gave a concise presentation of his formulation of the equations for the Green’s functions of quantum fields based on this novel approach to field quantization. Schwinger there introduced the use of “sources”—classical sources for Bosonic fields and Grassman anticommuting sources for Fermionic fields— as functional variables. Schwinger’s formulation was the functional differential equation version that in its integral form is called functional integration. The power of the approach stems from the fact that the symmetry properties of the Green’s functions can readily be exhibited, and approximation schemes can be devised that preserve these symmetry properties. Dating from the same period are his publication of the Schwinger action principle and, with Paul Martin, the use of temperature-dependent many-particle Green’s functions for addressing equilibrium and nonequilibrium problems in condensed matter physics. These contributions by Schwinger were widely appreciated and recognized. He was awarded the National Medal of Science in 1964. In 1951 he had already shared the first Albert Einstein Prize with Kurt Gödel.

**Source Theory** In the mid-1960s Schwinger started reformulating the foundations of fundamental physics and expressing them in a new framework: source theory. Source theory represented Schwinger’s efforts to replace the prevailing operator field theory by a philosophy and methodology that eliminated all infinite quantities. Schwinger’s objections to operator field theory stemmed at the pragmatic level from the fact that it seemed impossible to incorporate the strong interactions within its framework, and at the philosophical level that it made implicit assumptions about unknown phenomena at inaccessible, very high energies to make predictions at lower energies.

When the interactions are weak, as in the case of QED, it had been possible to go from a quantum field theoretic description to a particle description using the notions of renormalization. These can be interpreted as separating the effects of the experimentally inaccessible very high-energy dynamics from the effects that are experimentally accessible, and incorporating the former into a finite number of parameters values that are to be determined experimentally. However, when the interactions are strong, one has to deal with a possibly unlimited number of entities interacting with one another in a complicated manner, and it becomes nigh impossible to establish a correspondence between the observable particles and the fundamental fields. This failure indicated the need for new approaches to the strong interactions. However, the alternatives that were advanced were not acceptable to Schwinger. He found the S-matrix theory of Geoffrey Chew unacceptable because it lacked the specification of the dynamics involved; and he found the current algebra approach unsatisfactory because he was skeptical that one could obtain dynamical consequences from group theoretical kinematic assumptions. Encouraged by his success in using phenomenological “effective” Lagrangians in reproducing some of the low energy results of current algebra, Schwinger undertook to develop a phenomenological approach that would begin with robust knowledge about known phenomena at accessible energies and proceed to make predictions of physical phenomena at higher energies. The result was source theory.

For Schwinger, source theory was a mathematical description of laboratory practice that is conceptually sound and mathematically simple, a description that did not have any of the difficulties encountered in the quantum field theoretical operator formalism. It contained no divergent quantities, and thus there was no need for any renormalization procedures. And because all the parameters that appeared in the formulation were fixed initially, there were no new constants appearing when the class of phenomena under examination was enlarged. Despite its merits, Schwinger’s source theory fell on deaf ears. The attractive features of the quark model of hadrons; of the electroweak theory of Sheldon Glashow, Steven Weinberg, and Abdus Salam; and of quantum chromodynamics (QCD), and most importantly their predictions and experimental corroboration; had removed the appeal of the phenomenological aspects of source theory. Schwinger’s insistence on basing his theories on phenomenology had led him to reject both the quark model of hadrons and QCD. The notion of a “particle,” such as a quark, which was not describable by asymptotic states, was distasteful to him. His pursuit of source theory in the early 1970s—at the very time of the resurgence of QFT in the aftermath of the successes of the Glashow-Salam-Weinberg electroweak theory and of the proof by Gerard't Hooft that the Yang-Mills theory with a Higgs mechanism for breaking symmetry and giving masses to the particles is renormalizable—alienated him from the community and drove him out of the mainstream of modern physics.

**Quantum Field Theory** Schwinger’s alienation was aggravated by the fact that in February 1971 he left Harvard to accept a position at UCLA and had to establish ties to a new community with interests somewhat different from those of Cambridge, Massachusetts.

The chasm between Schwinger’s views and those of the community at large as set by the younger men who had achieved the breakthroughs (Glashow, Weinberg, Sidney Coleman, David Gross, Hooft) was too deep to be easily bridged. Schwinger was more modest in his approach. In 1965 in his contribution titled “The Future of Fundamental Physics,” to the volume *Nature of Matter: Purpose of High Energy Physics* that Luke Yuan edited, Schwinger had written that he believed that “the scientific level of any period is epitomized by the current attitude toward the fundamental properties of matter. The world view of the physicist sets the style of the technology and the culture of the society and gives direction to future progress.” For Schwinger fundamental physics was a way to understand human intervention into the physical world; therefore, the way in which it was formulated mattered deeply. For Schwinger quantum mechanics was only the mathematical symbolical representation of measurements in atomic physics, and similarly, source theory was the mathematical symbolism of human manipulations in high-energy physics.

When Schwinger left the mainstream of particle physics and challenged the foundations upon which the theoretical investigations were being carried out, his new endeavors were disdainfully set aside by the community as mistaken or irrelevant. Several of his research papers were rejected dismissively by *Physical Review Letters*. His response was to resign both as a member and as a Fellow of the American Physical Society. These experiences probably contributed to his involvement in unconventional projects such as cold fusion and sonoluminescence.

Starting in the 1980s, after teaching a course in quantum mechanics, Schwinger began a series of papers on the Thomas-Fermi model of atoms and, together with Berthold-Georg Englert, elaborated the approach. These contributions have been deemed important by the atomic physics community. His last scientific endeavor before his death in 1994 was attempting an explanation of sonoluminescence, the emission of light by bubbles in a liquid excited by acoustic waves. Schwinger died on 16 July 1994 of pancreatic cancer.

Schwinger’s lifetime work extends to almost every frontier of modern theoretical physics. He made far reaching contributions to nuclear, particle, and atomic physics; to statistical mechanics; to classical electrodynamics; to general relativity; and to the mathematical formulation of quantum theory. Many of the mathematical techniques that he developed are to be found in the tool kit of every theorist. He was one of the prophets and pioneers in the uses of gauge theories. His name is associated with many concepts and techniques in physics: the Tomonaga-Schwinger equation, the Lippmann-Schwinger equation, the Dyson-Schwinger equation, the Schwinger model, the Schwinger term, and the Kubo-Martin-Schwinger condition on finite-temperature Green’s functions. He was the advisor to some seventy-four doctoral students and over twenty postdoctoral fellows, many of whom became the outstanding theorists of their generation. The influence of Julian Schwinger on the physics of his time was profound.

## BIBLIOGRAPHY

*Schwinger’s Nachlass has been deposited in the Department of Special Collections at the University Research Library, University of California, Los Angeles. Kimball A. Milton’s introduction to the volume of seminal papers of Julian Schwinger that he edited*, A Quantum Legacy, *Singapore: World Scientific, 2000, is a concise, valuable overview of Schwinger’s works. It also contains informative comments on Schwinger’s papers. A list of Schwinger’s publications can be found in that volume, as well as in Jack Y. Ng's* Julian Schwinger: The Physicist, the Teacher, and the Man, *Singapore: World Scientific, 1996. An earlier selection of Schwinger’s papers is to be found in Moshe Flato, Christian Fronsdal, and Kimball A. Milton, eds*., Selected Papers (1937–1976) of Julian Schwinger, *Dordrecht, Netherlands: Reidel, 1979*.

### WORKS BY SCHWINGER

*Quantum Dynamics*. Part I. *Cours professé à l’École d’été de physique théorique, Les Houches*. Grenoble, France: Université de Grenoble, 1955.

*Quantum Electrodynamics*. New York: Dover Press, 1958.

With David Saxon. *Discontinuities in Waveguides*. New York: Gordon and Breach, 1968.

*Quantum Kinematics and Dynamics*. New York: Benjamin, 1970.

*Einstein’s Legacy: The Unity of Space and Time*. Scientific American Library, vol. 16. New York: W.H. Freeman, 1986.

*Particles, Sources and Fields*. 3 vols. Redwood City, CA: Addison-Wesley, 1989.

*Quantum Mechanics: Symbolism of Atomic Measurements*. Edited by Berthold-Georg Englert. Berlin: Springer Verlag, 2001.

### OTHER SOURCES

Mehra, Jagdish, and Kimball A. Milton. *Climbing the Mountain: The Scientific Biography of Julian Schwinger*. New York: Oxford University Press, 2000.

Ng, Y. Jack. *Julian Schwinger: The Physicist, the Teacher, and the Man*. Singapore: World Scientific, 1996.

Schweber, Silvan S. *QED and the Men Who Made It*. Princeton, NJ : Princeton University Press, 1994.

*Silvan S. Schweber*

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**Schwinger, Julian Seymour**