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Photograph courtesy of Clarice Schwinger.

JULIAN SCHWINGER February 12, 1918âJuly 16, 1994 BY PAUL C. MARTIN AND SHELDON L. GLASHOW j ulian schwinger, who died on July 16, 1994, at the age of 76, was a phenomenal theoretical physicist. Gentle but steadfastly independent, quiet but dramatically eloquent, self- taught and self-propelled, brilliant and prolific, Schwinger remained active and productive until his death. His ideas, discoveries, and techniques pervade all areas of physics. Schwinger burst upon the scene meteorically in the late 1930s, and by the mid-20th century his reputation among physicists matched those of earlier giants. To a public vaguely conscious of relativity and quantum uncertainty but keenly aware of nuclear energy, the New York Times reported in 1948 that theorists regarded him as the heir apparent to Einsteinâs mantle and his work on the interac- tion of energy and matter as the most important develop- ment in the last 20 years. With the development of powerful new theoretical methods for describing physical problems, his influence grew. In the early 1950s the Journal of Jocular Physics, a publication of the Bohr Institute for Theoretical Physics in Copenhagen, included a template for articles by aspiring theorists. It began âAccording to Julian Schwingerâ and invoked âthe Greenâs function expression for â¦â. References to unpublished Schwinger lecture notes and some classic Schwinger papers followed. The recipe elicited 333

334 BIOGRAPHICAL MEMOIRS smiles, but it accurately portrayed his preeminence at that time. With this preeminence came stratospheric expectations, which he continually strove to fulfill. Schwinger was born in upper Manhattan on February 12, 1918. He went to P.S. 186, to Townsend Harris High School (then New York Cityâs leading public high school), and to the College of the City of New York, following brother Har- old by six years. Harold was the outstanding student, the valedictorian, their mother would explain. Julian took the establishment of teachers, textbooks, and assignments less seriously. From some, most notably physics teacher Irving Lowen, he benefited greatly. But there were better things to do with the 11th edition of the Encyclopaedia Britannica and the books and journals in nearby libraries. In 1926 when Werner Heisenberg and Paul Dirac were developing quantum mechanics, Schwinger was in the third grade. Eight years later, before completing high school, he had assimilated these ideas and in an unpublished paper extended Diracâs ideas to many-electron systems. By then, word of the wunderkind had spread among graduate students at City College, where he enrolled in the fall of 1934 and at Columbia University, to whichâthanks to that institutionâs support and the subsequent intervention of I. I. Rabiâhe was able to transfer in 1936. In a remarkable letter dated July 10, 1935, from Hans Bethe to I. I. Rabi, Bethe describes his meeting with Schwing- er: I entirely forgot that he [Schwinger] was a sophomore 17 years of age. . . His knowledge of quantum electrodynamics is certainly equal to my own, and I can hardly understand how he could acquire that knowledge in less than two years and almost all by himself.â Bethe concludes that âSchwinger will develop into one of the worldâs foremost theoretical physicists if properly guided, i.e., if his curriculum is largely left to his own free choice.

julian schwinger 335 Less than four years after he entered college Schwinger had completed both the requirements for his undergraduate and graduate degrees and the research for his doctoral thesis. During his sophomore year, with Otto Halpern, he predicted the polarization of electrons by double scattering and with Lloyd Metz he computed the lifetime of the neutron. On his own as a junior he computed how neutrons were polar- ized by double scattering from atomic electrons. That the electron current must be treated relativistically by the Dirac equation (that is, that the classical approximations made by Felix Bloch were inadequate) was noted sotto voce. Next, he calculated the influence of a rotating magnetic field on a spin of any magnitude j. His analysis for j = 1/2 remains the prototype for all discussions of transitions in two-level systems by âRabi flipping.â During the spring of 1937, he and Edward Teller studied coherent neutron scattering by hydrogen molecules, showing how the spin-dependent, zero-energy, neutron-proton-scatter- ing amplitudes could be determined from the experimental data. This topic was the theme of his doctoral thesis. In the fall of 1937, with his undergraduate degree in hand, eight significant papers published, and his doctoral thesis virtually complete, Schwinger left New York, planning to spend the fall term at the University of Wisconsin with Gregory Breit and Eugene Wigner, and the spring term at the University of California, Berkeley, with J. Robert Oppen- heimer. In Madison he took such great pleasure in working at night on problems of his own choosing that he stayed for the entire year. He would maintain this nocturnal regimen for most of his career. Schwinger returned to Columbia for 1938-1939. As house theorist he worked with Hyman Henry Goldsmith, John Manley, Victor Cohen, and Morton Hammermesh

336 BIOGRAPHICAL MEMOIRS on nuclear-energy-level widths and on the neutron-proton interaction and with Rabi and his associates on molecular beams. His doctoral degree under Rabiâs supervision was awarded in 1939. Schwinger spent the next two years at Berkeley working with Oppenheimer, students, and visitors (Herbert Corbett, Edward Gerjuoy, Herbert Nye, and William Rarita). With Rarita he determined definitively the effects of the tensor force on the deuteronâs magnetic and quadrupole moments. He also examined the consequences of tensor and exchange forces between pairs of nucleons on the magnetic and quad- rupole moments of light nuclei, nuclear pair emission, deu- teron photodisintegration, and other phenomena. The Rarita-Schwinger equationâone of the few of his many contributions that bear his nameâwas all but forgotten for many years. But this generalization of the Dirac equation to particles with spin 3/2, and the study of its invariances when the particles are massless, has been recalled by theorists who postulate a gravitino, a spin-3/2 fermion supersymmetric partner of the graviton. Notwithstanding a ticker tape parade for Albert Einstein, theoretical physics held little fascination for the American public or major American universities prior to the Second World War. Even so, in 1941 the nationâs great universities might have been expected to compete fiercely for an ac- knowledged young genius who lectured along with Wolfgang Pauli, Frederick Seitz, and Victor Weisskopf at the world- famous Michigan summer school for physics. They did not. In some cases, a long tradition of anti-Semitism may have been a factor. Schwinger was offered and accepted a lowly instructorship at Purdue University with just one concession to his preferred work schedule: His introductory physics sec- tion would start at noon.

julian schwinger 337 Led by first-rank physicist Karl Lark-Horovitz, Purdue attracted able graduate students and postdoctoral fellows. Among them was Robert Sachs, who (as related by Sylvan Schweber in his book on QED) recalled that in February 1942, âWe had to spend the whole time trying to cheer Julian upâ at his 24th birthday party âbecause he had not yet made the great discovery expected of him.â Along with physicists at Cornell University and the Uni- versity of Rochester and with colleagues at Purdue, Schwinger spent the first year and a half of World War II working on the properties of microwave cavities. The work was coordinated with and supported by MIT Radiation Laboratory research projects. Invited by Oppenheimer to join the Manhattan Project, Schwinger spent the summer of 1943 at the University of Chicagoâs Metallurgical Laboratory, where John Wheeler, Eugene Wigner, and other scientists were designing the first Hanford reactor. As in Madison, Schwinger worked nights, and so Bernard Feld (who had worked with him at Columbia) decided to work an intermediate afternoon-evening shift so that he might help link Schwinger with those working normal hours. After âa brief sojourn to see if I wanted to help develop the BombâI didnât,â recalled Schwinger, âI spent the war years helping to develop microwave radar.â Reluctance to follow othersâ agendas once again helped determine his course. Thus, in the fall of 1943 after most luminaries with nuclear expertise had left the MIT Rad Lab for Los Alamos, Schwinger arrived in Cambridge with little notion that he would remain in the area for more than a quarter century. Many of Schwingerâs colleagues during his three-year stint at the Rad Lab became his lifelong friends. Among them were Harold Levine from Cornell; Nathan Marcuvitz, an electrical engineer from Brooklyn College; and David

338 BIOGRAPHICAL MEMOIRS Saxon, an MIT graduate student. Schwingerâs collaboration with Levine led to a series of papers that creatively used variational methods and Greenâs functionsâtwo approaches central to so much of Schwingerâs workâto obtain important new results on radiation and diffraction. Schwinger and Marcuvitz appreciated the value of integral equation formulations of waveguide theory that incorporate the boundary conditions accompanying partial differential equation formulations and can be cast in the engineering language of transmission lines and networks. The isolation of complex internal properties of components and the characterization of these components through a small set of parameters provided valuable insightsâinsights that would later prove valuable in characterizing nuclear phenomena via effective range theory, scattering matrices, and new formal approaches to complex scattering processes. At the Rad Lab Schwinger gave a series of lectures on microwave propagation for which David Saxon served as his Boswell. Many of the ideas and techniques in them re- cur in his later theoretical work on quantum mechanics, electrodynamics, nuclear physics, and statistical mechanics. A small volume, titled Discontinuities in Waveguides, contain- ing some of these lectures, was published decades later. In the volumeâs introduction and 138 pages of text, Schwinger himself observed that the name âGreenâ or simply âGâ (for Greenâs function) appeared more than 200 times. Some powerful relations imposed on scattering amplitudes by time reversibility and energy conservation can also be traced back to Schwingerâs work at the time. When the War ended, Schwingerâs attention turned to the physics of high-energy accelerators and to the obstacles to producing them. It struck him that the energy loss of a highly relativistic electron accelerating in a circular orbit could be simply and straightforwardly deduced from the covariant

julian schwinger 339 expression for radiation damping, making the fourth power law for the radiated energy transparent. âManifest covari- anceâ would play an important role in Schwingerâs work on quantum electrodynamics. During this period, Schwinger also designed a novel accelerator, later named the minotron. In addition to work on other aspects of synchrotron ra- diations, notepads in his desk drawers at that time included studies of neutron scattering in a Coulomb field, and a group-theory-free approach to the properties of angular momentum that expresses angular momentum operators in terms of oscillator creation and annihilation operators. On Angular Momentum, a set of his notes that makes exhaustive use of this approach, circulated widely for 15 years prior to its publication in 1965. Schwingerâs long and diverse bibliography, with more than 200 publications, contains no publications over the period 1942 through 1946. However, the war produced sweeping changes in the social and intellectual values and mores of the public and the nationâs premier universities. Thus, in February 1946, the month Schwinger turned 28, he was of- fered and accepted a tenured position at Harvard. Profes- sorship offers from Columbia and Berkeley soon followed, but he turned them down. Students attending topflight universities were also dif- ferent before and after the war. Postwar students included mature veterans whose studies had been interrupted by the war and bright youth from a broader cross-section of the nationâs preparatory schools. Doors were open, for example, to outstanding students from New Yorkâs select high schools (for example, Bronx Science, Brooklyn Tech, and Stuyves- ant, the successors to Schwingerâs alma mater, Townsend Harris). Schwingerâs first year at Harvard, 1946-1947, was a busy one. He offered courses on waveguides and theoretical

340 BIOGRAPHICAL MEMOIRS nuclear physics, and accepted a number of graduate stu- dents whom he set to work on a wide range of problems. Among these early students were Bernard Lippmann who investigated integral equation formulations of scattering theory (Lippmann-Schwinger equations); Walter Kohn, who studied variational principles for scattering; Ben Mottelson, who worked on the properties of light nuclei; Bryce DeWitt, who explored gravitation and the interaction of gravitation with light; and Roy Glauber, who examined meson-nucleon interactions and mesonic decay. He and longtime friend Herman Feshbach pursued their studies of the internucleon potential. When the academic year ended, Schwinger and 22 other physicists headed off to the Shelter Island conference on the foundations of quantum physics, where the electrodynamic origin of the spectral lineshift measured by Willis Lamb and Robert Retherford was discussed. Legend has it that Weisskopf and Schwinger proposed that in the Dirac theory compensating effects of electrons and positrons could lead to a cancellation of divergences, and that Hans Betheâon his way home from the conferenceârecognized that the bulk of the effect could be estimated nonrelativistically. Four days after the conference ended, Schwinger married Clarice Carroll, whom he had been courting for several years and with whom he would share the next 47 years. Schwingerâs lectures, from his early days at Harvard on, have been likened to concerts at which a virtuoso performs pieces brilliantly. Each lecture was an event. Speaking elo- quently, without notes, and writing deftly with both hands, Schwinger would weave original examples and profound insights into beautiful patterns. Audiences would listen rever- ently seeking to discern the unheralded difficult cadenzas. As at a concert, interruptions to the flow were out of place.

julian schwinger 341 Schwingerâs masterly performances were not limited to the Harvard community. His audiences quickly grew to in- clude faculty and students from throughout the Boston area. Notes taken by John Blatt, an MIT instructor, were shipped to a team of Princeton graduate students, who in swift relays copied them onto duplicator masters for reproduction. Un- derground notes in multiple handwritings, with some pages containing picturesque mistranscriptions (such as âmilitary matricesâ for âunitary matricesâ) spread quickly throughout the country and overseas. Schwinger was never satisfied with his expositions. Each time he offered a course he carefully reworked and honed his ideas, methods, and examples, presenting them in a new way, a way that differed from his earlier versions circulating in othersâ articles and lecture notes, often without attribu- tion. Significant portions of many classic texts on nuclear physics, atomic physics, optics, electromagnetism, statistical physics, quantum mechanics, and quantum field theory can be traced to one or another version of his lectures. As noted, a few isolated gemsâhis work on microwaves and his notes on angular momentumâwere eventually pub- lished. He was also stimulated in 1964 âto rescue from the quiet death of lecture notesâ a beautiful discussion of Cou- lomb Greenâs functions âworked out to present to a quantum mechanics course given in the late 1940s.â The bound-state momentum space wave functions are deftly and concisely constructed as four-dimensional spherical harmonics. Notes for his early quantum mechanics courses also include elegant and revealing unpublished treatments of Coulomb scattering and of the unusual way that the Stark effect lifts hydrogenic degeneracies. These and other jew- els may be found in the archives assembled by UCLA of lecture notes, chapters, and preliminary editions of books on quantum mechanics, field theory, and electromagnetism

342 BIOGRAPHICAL MEMOIRS that failed to meet his exacting standards. A few appear in Classical Electrodynamics, published in 1998. Not until September 1947 did Schwinger begin to work on the electrodynamic effects responsible for deviations of experimental observations from values predicted by the Dirac equation. Hyperfine structure measurements of hydrogen, deuterium, and tritium by John Nafe, Edward Nelson, and Rabi indicated a 0.12 percent error in the electronâs mag- netic moment, and measurements by Lamb and Retherford displayed a splitting of about 1050 megacycles between states of the hydrogen atom with degenerate Dirac energies. âBy the end of November I had the results,â Schwinger later recalled. He described them to a capacity audience at an American Physical Society meeting at Columbia University on a Saturday morning in January 1948, giving a command repeat performance to an overflow audience that afternoon. He discussed his calculations in fuller detail at the Pocono conference in the spring and in lectures at the University of Michigan summer school. Demonstrating his computational virtuosity, he published his reformulation of quantum elec- trodynamics in three long papers in Physical Review, Quantum Electrodynamics I (1948), II (1949), and III (1949). They include several of the results for which he, Richard Feynman, and Sin-Itiro Tomanaga were eventually awarded the 1965 Nobel Prize in Physics. To those who admire the eloquence of Schwingerâs expositions, it seems ironic that these three uncharacteristically opaque papers should have helped secure his place in Nobel history. In light of his many spectacular achievements, including his fundamental contributions to quantum electrodynamics, Schwinger was elected to the National Academy of Sciences at the exceptionally young age of 31. By 1950 Schwinger recognized the need for a more system- atic approach to quantum field theory utilizing a covariant

julian schwinger 343 quantum version of Hamiltonâs principle. In 1951 in a pair of brief papers in the Proceedings of the National Academy of Sciences, the techniques and concepts on which field theorists all rely made their appearance. Using âsourcesâ as fundamental variables, Schwinger provided the functional differential equation version of what in integral form is now called functional integration. Of lasting importance, much of this material has been rediscovered by others. For theoretical students at Harvard at the time, Schwingerâs techniques pro- vided an Aladdinâs lamp for parsing, analyzing, and solving problems. As a matter of principle, these papers noted, The temporal development of quantized fields is described by propagation functions, or Greenâs functions. The construction of these functions for coupled fields is usually considered from the viewpoint of perturbation theory. Although the latter may be resorted to for detailed calculations, the formal theory of Greenâs functions should not be based on the assumption of expandability in powers of the coupling constant. After relating the outgoing wave boundary condition to the vacuum, the second paper defined functions (such as self- energies and effective interactions) that characterize exactly (that is, not as power series in the coupling constant) the propagation and interaction of quantum fields. This approach opened the way for major conceptual and computational advances in quantum electrodynamics. A series of papers called âTheory of Quantized Fieldsâ followed. Word appears to have circulated that the stress Schwinger placed on the properties of fields that transcended perturba- tion theory, and his personal dislike of diagrams disadvantaged those working for and with him in the 1950s. Hardly! His students and postdoctoral fellows were fully conversant and facile with the diagrammatic approaches of Feynman and Freeman Dyson and analytic approaches. With Schwingerâs tools, they generated directly and succinctly the connected diagrams involving dressed propagators that describe vari-

344 BIOGRAPHICAL MEMOIRS ous processes. With them they evaluated a large share of the quantum electrodynamic corrections to hydrogen and positronium bound states and a large share of the higher order corrections (for example, to the electronâs magnetic moment) computed at that time. Other aspects of Schwingerâs routine can also mistakenly be cast in an unkindly light. It is true, for example, that stu- dents might wait a long time to see him during his lengthy office hours. He could have spent less time with each and he could have accepted fewer. In his first year at Harvard he accepted 10 graduate students, and in subsequent years no one recalls his ever turning down a prospective student whom the department certified as qualified. When requested, Schwinger posed problems to students, sometimes offering them and colleagues his notes. At the same time, he welcomed students who preferred to formulate their own thesis topics. If students told him they were stuck, he would offer sugges- tions and proposals on the spot and at subsequent meetings. Rare are the students who did not cherish their interactions with Schwinger in sessions that were often lengthy. His late arrival for classes was not because he left gath- ering materials for his lecture to the last minute. Not only in the early years but also throughout his long career he insisted on remaining home the night before each lecture, staying up late to prepare exactly what he would say and how best to say it. Among the giant figures in theoretical physics, his level of commitment to course lectures and to the supervision of large numbers of research students may be unmatched. Schwingerâs investigations of quantum field theory con- tinued through the 1950s. Relativistic invariance and gauge invariance constrain the formally divergent expressions ap- pearing in quantum electrodynamics calculations. Colleagues of Pauli, ignoring the consequences of gauge invariance, had

julian schwinger 345 recast and manipulated these expressions to predict a finite photon mass. Schwingerâs 1951 paper on vacuum polarization and gauge invariance addressed some of these issues with a novel and elegant proper-time formalism. The nonpertur- bative properties of a Dirac field coupled to a prescribed external electromagnetic field, first derived in this paper, are still widely used and admired. Schwinger saw that many ambiguities associated with interacting quantum fields lay in the treatment of formal expressions for composite opera- tors such as currents. Indeed, the âtriangle anomaliesâ that play a major role in modern (post-1969) field theory were first identified here and studied further by Schwinger and Ken Johnson during the 1950s. Further studies of quantized fields led in 1958 to Schwingerâs important series of papers on âSpin, Statistics, and the TCP Theorem.â During the 1950s, puzzles posed by elementary particle physics preoccupied Schwinger. What role could strange particles, whose properties were just being elucidated, play in the grand scheme of things? He was convinced that the answer had to do with their transformation properties under a generalization of isotopic-spin symmetry, which he took to be the four-dimensional rotation group. The group genera- tors, under commutation, defined what would later become known as the âalgebra of charges.â Schwinger gathered particle species together, both strange and nonstrange, into representations of his proposed group. In this manner the otherwise mysterious Gell-Mann-Nishijima formulaâwhich relates charge, hypercharge, and isospinâhad a natural explanation. It later turned out that Schwingerâs intuition was correct, although his choice for the relevant transformation was not. The approximate symmetries of mesons and baryons were not shared by the leptons. For these particles, Schwinger proposed a direct analog to isospin. Just such a group was

346 BIOGRAPHICAL MEMOIRS later to become an integral part of todayâs successful elec- troweak theory. The known leptonsâin Schwingerâs per- versely original interpretationâwere to form a weak isospin triplet: {Î¼+, Î½, eâ}. An immediate consequence of this notion was the selection rule forbidding Î¼âe + Î³ and the obliga- tory distinction between neutrinos associated with electrons and muons. âIs there a family of bosons that realizes the T=1 symmetry of [the lepton symmetry group]?â Schwinger asked. If so, the charged counterparts of the photon could mediate the weak interactions. Both the vectorial nature of the weak force and its apparent universality would arise as simple consequences of the underlying symmetry structure. He also suggested that vacuum expectation values of scalar fields could provide a way of breaking symmetries and giving fermions their masses. Schwingerâs 1957 paper on particle symmetries appeared at a time of rapid progress and great confusion, between the discoveries of parity violation and the V-A nature of the weak interactions. His ambitious paper concluded with the modest suggestion that âit can be of value if it provides a convenient frame of reference in seeking a more coherent account of natural phenomena.â For some of the theorists who developed that coherent theory over the next 15 years, it did just that. Schwinger himself, however, turned to other problems. A 1959 paper with Martin extended Schwingerâs nonper- turbative field theoretic concepts and methods for the vacuum state to material systems in equilibrium at nonvanishing densi- ties and temperatures, and a 1961 paper, camouflaged by the title âBrownian Motion of a Quantum Oscillatorâ paved the way for the study of systems far from thermal equilibrium. Extended by K. T. Mahantappa, Pradip Bakshi, and Victor Korenman at Harvard, and rediscovered (independently) by Leonid Keldysh, Schwingerâs âtwo-timeâ approach is now

julian schwinger 347 widely used in studies of cosmology, quark-gluon plasmas, and microelectronic devices. As indicated above, Schwinger recognized in the early 1950s that the composite operators for observables must be treated with care. Naive manipulations with canonical commutation relations suggest that the space and time components of a current commute with each other. In 1959 Schwinger published an argument, dazzling in its simplicity, that moved this problem to the fore and identified a class of anomalies, now called âSchwinger terms.â He followed it in papers directed toward the gravitational field with a study of the conditions imposed by consistency on stress tensor com- mutation relations. Today we recognize the key roles such terms play in particle physics and statistical mechanics. In the late 1960s Schwinger directed much of his attention to his source theory. The motivation was clear. In spite of field theoryâs many triumphs, the prospects then seemed dim for predicting the results of experiments involving strongly interacting particles from a unified field theory. Prospects for a renormalizable theory of the electroweak interactions also seemed dim. Why not try to develop a theory that would progress in the same way as experimentâfrom lower to higher energies? Source theory provided a framework for pursuing this modest goal. Soon thereafter these prospects brightened. Gauge field theories were shown to be renormalizable and consonant with an increasing number of phenomena. Quantum field theory, to which Schwinger had contributed so much, might describe all strong and electroweak phenomena. Schwinger demurred, remaining steadfastly committed to the source theory approach that he and his students were pursuing. The philosophical basis of divergence-free âanabaticâ (going up) phenomenological source theory was, he maintained, immensely different from âthe speculative approach of

348 BIOGRAPHICAL MEMOIRS trickle-downâ field theory. So too were its predictive powers. He espoused this contrarian position steadfastly. During the 1960s, Schwingerâs lifestyle expanded in other ways. He began playing tennis regularly, and he and Clarice spent time in distant places, including Paris and Tokyo. In 1971 the Schwingers left Harvard and their Belmont home for UCLA and the Bel Aire hills. In sunny southern Califor- nia, with students, new collaborators, and longtime friends, Schwinger continued working on source theory (âsourceâ appears in the title of more than 15 publications) and contrib- uting significantly to a host of interesting physical problems not in vogue. With Lester DeRaad Jr. and Berthold-Georg Englert, he explored statistical models of the atom that extend the Fermi-Thomas approximation and, with Kimball Milton and DeRaad, various aspects of the Casimir effect. In his new surroundings he published more than 70 papers. Reports of cold fusion whetted his contrarian appetite. The publicized experiments might be flawed, he would observe, but fundamental physical principles do not rigorously exclude the possibility that without tokamaks and high-temperature plasmas, somehow, in some way, in some material, the energy required for fusion might be coherently concentrated and transferred from atoms to nuclei. One of Schwingerâs last papers is a 1993 talk titled âThe Greening of Quantum Field Theory: George and I, Lecture at Nottingham, July 14, 1993.â It contains the count of refer- ences to Green in Discontinuities in Waveguides mentioned earlier and a recital of a multitude of the linkages with George Green of Schwingerâs research on field and particle theory, statistical mechanics, through to work on the Casimir effect and sonoluminescence. Although Schwingerâs genius was widely recognized immediately, and Greenâs very slowly. Schwinger concludes his talk by answering the question,

julian schwinger 349 âWhat then shall we say about George Green?â with âHe is, in a manner of speaking, alive, well, and living among us.â That, too, can be said for Schwinger. Schwingerâs legacy has also been greatly amplified by the 70 doctoral students and 20 postdoctoral fellows who worked with him. For their research they have innumerable major awards, including four Nobel prizes; nine of his students have been elected to the National Academy of Sciences. Two features shared by Schwingerâs professional off- spring are striking: the diversity of their specialties and the consistently high regard and great debt they express for his mentorship. The group includes leaders in particle theory, nuclear physics, astrophysics, gravity, space physics, optics, atomic physics, condensed matter physics, electromagnetic phenomena, applied physics, mathematics, and biology. It also includes many who, like Schwinger, have worked in a variety of fields, mirroring Schwingerâs own broad interests and his passion for seeking patterns and paradigms that put new facts in proper perspective. Their recollections are remarkably uniform. While few former students considered him a close friend, almost all speak fondly of his kindness and generosity. He was consid- erate and willing to do his best to provide scientific advice when he thought help was needed. His insight and sugges- tions were often decisive. By example he conveyed lofty aspirations: to approach every problem in a broad context, with as few assumptions as possible; to seek new and verifiable results and to present them as elegantly as possible; to avoid energy- and time- consuming political maneuvering; to understand, extend, unify, and generalize; and to reveal the hidden beauty of nature. Walter Kohn spoke for all of Schwingerâs students in saying,

350 BIOGRAPHICAL MEMOIRS We carried away the self-admonition to try and measure up to his high stan- dards; to dig for the essential; to pay attention to the experimental facts; to try to say something precise and operationally meaningful, even ifâas is usualâone cannot calculate everything a priori; not to be satisfied until ideas have been embedded in a coherent, logical and aesthetically satisfy- ing structure. Schwinger also had a remarkable knowledge of matters nonscientific and a gentle humor. While too reserved to savor media stardom, he enjoyed presenting relativity to a wide audience in a popular book and on BBC television. He was always willing to lend his name and support to worthy causes. Fond recollections of the hospitality, warmth, and interest displayed by both Julian and Clarice Schwinger abound. An article about Julian Schwinger was published by the authors of this memoir in Physics Today, Oct. 1995, pp. 40-46, under the copyright of the American Institute of Physics. With AIP permission the authors have presented here a slightly modified version of that article.

julian schwinger 351 SELECTED BIBLIOGRAPHY 1935 With O. Halpern. On the polarization of electrons by double scat- tering. Phys. Rev. 48:109. 1937 On the magnetic scattering of neutrons. Phys. Rev. 51:544-552. On the non-adiabatic processes in inhomogeneous fields. Phys. Rev. 51:648-651. With E. Teller. The scattering of neutrons by ortho and para hydro- gen. Phys. Rev. 51:775. On the spin of the neutron. Phys. Rev. 52:1250. 1941 With W. Rarita. On the neutron-proton interaction. Phys. Rev. 59:436- 452. With R. Rarita. On a theory of particles with half-integral spin. Phys. Rev. 60:61. 1946 Electron radiation in high energy accelerators. Phys. Rev. 70:798. 1947 A variational principle for scattering problems. Phys. Rev. 72:742. 1948 On quantum electrodynamics and the magnetic moment of the electron. Phys. Rev. 73:416-441. Quantum electrodynamics. I. A covariant formulation. Phys. Rev. 74:1439-1461. 1949 Quantum electrodynamics. II. Vacuum polarization and self-energy. Phys. Rev. 75:651-679. Quantum electrodynamics. III. The electrodynamic properties of the electron Phys. Rev. 76:790.

352 BIOGRAPHICAL MEMOIRS 1950 With B. Lippman. Variational principles for scattering processes. I. Phys. Rev. 79:469-480. 1951 On gauge invariance and vacuum polarization. Phys. Rev. 82:664- 679. On the Greenâs functions of quantized fields. I, II. Proc. Natl. Acad. Sci. U. S. A. 37:452-459. 1958 Spin, statistics and the TCP theorem. Proc. Natl. Acad. Sci. U. S. A. 44:223-228, 617-619. 1959 With P. C. Martin. Theory of many-particle systems. I. Phys. Rev. 115:1342-1373. Field theory commutators. Phys. Rev. Lett. 3:269. 1961 Brownian motion of a quantum oscillator. J. Math. Phys. 2:407. 1963 Commutation relations and conservation laws. Phys. Rev. 130:406- 409. 1964 Coulomb Greenâs function. J. Math. Phys. 5:1606. 1965 Quantum Theory of Angular Momentum (eds. L. Biedenharn and H. van Dam). New York: Academic Press. 1966 Magnetic charge and quantum field theory. Phys. Rev. 144:1087- 1093.

julian schwinger 353 1968 With D. Saxon. Discontinuities in Wave Guides. New York: Gordon and Breach. 1970 Particles, Sources, and Fields. I. Reading, Mass.: Addison-Wesley. 1973 Particles, Sources, and Fields. II. Reading, Mass.: Addison-Wesley. 1978 With L. L. DeRaad Jr. and K. A. Milton. Casimir effect in dielectrics. Ann. Phys. 115(1):1-23. 1985 With B. G. Englert. Semiclassical atom. Phys. Rev. A 32:26-35. 1986 Einsteinâs Legacy: The Unity of Space and Time. New York: W. H. Free- man and Co. 1996 The Greening of Quantum Field Theory: George and I, Lecture at Nottingham, July 14, 1993. Printed in Julian Schwinger: The Physicist, the Teacher, the Man, ed. Y. J. Ng. Singapore: World Scientific.