分享

Julian Schwinger 1 9 1 8 — 1 9 9 4 A Biographical Memoir

 忧郁的诗 2011-06-11

national academy of sciences

Julian Schwinger

1 9 1 8 — 1 9 9 4

A Biographical Memoir by

p a u l c . m a r t i n a n d s h e l d o n l . g l a s h o w

Any opinions expressed in this memoir are those of the authors

and do not necessarily reflect the views of the

National Academy of Sciences.

Biographical Memoir

Copyright 2008

national academy of sciences

washington, d.c.

 JULIAN SCHWINGER

February 12, 1918–July 16, 1994

BY PAUL C. MARTIN AND SHELDON L. GLASHOW

julian 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, selftaught

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 Einstein’s mantle and his work on the interaction

of energy and matter as the most important development

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 “According to Julian Schwinger”

and invoked “the Green’s function expression for …”.

References to unpublished Schwinger lecture notes and

some classic Schwinger papers followed. The recipe elicited

B IOGRAPHICAL 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 City’s leading public high school), and to

the College of the City of New York, following brother Harold

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 Dirac’s 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 which—thanks to that institution’s

support and the subsequent intervention of I. I. Rabi—he

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 Schwinger:

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.” Bethe concludes that “Schwinger will

develop into one of the world’s foremost theoretical physicists if properly

guided, i.e., if his curriculum is largely left to his own free choice.

j u l i a n s chwi n g e r

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 polarized

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 “Rabi flipping.”

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-scattering

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 Oppenheimer.

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

B IOGRAPHICAL 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 Rabi’s 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 deuteron’s magnetic and quadrupole moments.

He also examined the consequences of tensor and exchange

forces between pairs of nucleons on the magnetic and quadrupole

moments of light nuclei, nuclear pair emission, deuteron

photodisintegration, and other phenomena.

The Rarita-Schwinger equation—one of the few of his

many contributions that bear his name—was 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 nation’s great universities

might have been expected to compete fiercely for an acknowledged

young genius who lectured along with Wolfgang

Pauli, Frederick Seitz, and Victor Weisskopf at the worldfamous

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 section

would start at noon.

j u l i a n s chwi n g e r

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, “We had to spend the whole time trying to cheer Julian

up” at his 24th birthday party “because he had not yet made

the great discovery expected of him.”

Along with physicists at Cornell University and the University

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.

I nvited by Oppenheimer to join the Manhattan Project,

Schwinger spent the summer of 1943 at the University of

Chicago’s 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 “a brief sojourn to see if I wanted to help develop

the Bomb—I didn’t,” recalled Schwinger, “I spent the war

years helping to develop microwave radar.” Reluctance to

follow others’ 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.

M any of Schwinger’s 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

B IOGRAPHICAL MEMOIRS

Saxon, an MIT graduate student. Schwinger’s collaboration

with Levine led to a series of papers that creatively used

variational methods and Green’s functions—two approaches

central to so much of Schwinger’s work—to 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 insights—insights 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 recur

in his later theoretical work on quantum mechanics,

electrodynamics, nuclear physics, and statistical mechanics.

A small volume, titled Discontinuities in Waveguides, containing

some of these lectures, was published decades later. In

the volume’s introduction and 138 pages of text, Schwinger

himself observed that the name “Green” or simply “G” (for

Green’s 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 Schwinger’s work at the time.

When the War ended, Schwinger’s 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

j u l i a n s chwi n g e r

expression for radiation damping, making the fourth power

law for the radiated energy transparent. “Manifest covariance”

would play an important role in Schwinger’s 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 radiations,

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.

Schwinger’s 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 nation’s premier universities. Thus, in

February 1946, the month Schwinger turned 28, he was offered

and accepted a tenured position at Harvard. Professorship

offers from Columbia and Berkeley soon followed,

but he turned them down.

Students attending topflight universities were also different

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

nation’s preparatory schools. Doors were open, for example,

to outstanding students from New York’s select high schools

(for example, Bronx Science, Brooklyn Tech, and Stuyvesant,

the successors to Schwinger’s alma mater, Townsend

Harris).

Schwinger’s first year at Harvard, 1946-1947, was a busy

one. He offered courses on waveguides and theoretical

10 B IOGRAPHICAL MEMOIRS

nuclear physics, and accepted a number of graduate students

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 Bethe—on

his way home from the conference—recognized 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.

Schwinger’s 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 eloquently,

without notes, and writing deftly with both hands,

Schwinger would weave original examples and profound

insights into beautiful patterns. Audiences would listen reverently

seeking to discern the unheralded difficult cadenzas. As

at a concert, interruptions to the flow were out of place.

j u l i a n s chwi n g e r 11

Schwinger’s masterly performances were not limited to

the Harvard community. His audiences quickly grew to include

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. Underground

notes in multiple handwritings, with some pages

containing picturesque mistranscriptions (such as “military

matrices” for “unitary matrices”) 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 others’ articles and lecture notes, often without attribution.

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 gems—his work on microwaves

and his notes on angular momentum—were eventually published.

He was also stimulated in 1964 “to rescue from the

quiet death of lecture notes” a beautiful discussion of Coulomb

Green’s functions “worked out to present to a quantum

mechanics course given in the late 1940s.” 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 jewels

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

12 B IOGRAPHICAL 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 electron’s magnetic

moment, and measurements by Lamb and Retherford

displayed a splitting of about 1050 megacycles between states

of the hydrogen atom with degenerate Dirac energies. “By

the end of November I had the results,” 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 electrodynamics

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 Schwinger’s 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 systematic

approach to quantum field theory utilizing a covariant

j u l i a n s chwi n g e r 13

quantum version of Hamilton’s 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 “sources” 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, Schwinger’s techniques provided

an Aladdin’s 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 Green’s 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 Green’s 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 selfenergies

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 “Theory of Quantized Fields” followed.

Word appears to have circulated that the stress Schwinger

placed on the properties of fields that transcended perturbation

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 Schwinger’s

tools, they generated directly and succinctly the connected

diagrams involving dressed propagators that describe vari14

B IOGRAPHICAL 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 electron’s magnetic

moment) computed at that time.

Other aspects of Schwinger’s routine can also mistakenly

be cast in an unkindly light. It is true, for example, that students

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 suggestions

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 gathering

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.

Schwinger’s investigations of quantum field theory continued

through the 1950s. Relativistic invariance and gauge

invariance constrain the formally divergent expressions appearing

in quantum electrodynamics calculations. Colleagues

of Pauli, ignoring the consequences of gauge invariance, had

j u l i a n s chwi n g e r 15

recast and manipulated these expressions to predict a finite

photon mass. Schwinger’s 1951 paper on vacuum polarization

and gauge invariance addressed some of these issues with a

novel and elegant proper-time formalism. The nonperturbative

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 operators

such as currents. Indeed, the “triangle anomalies” 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 Schwinger’s important series of papers

on “Spin, Statistics, and the TCP Theorem.”

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 generators,

under commutation, defined what would later become

known as the “algebra of charges.”

Schwinger gathered particle species together, both strange

and nonstrange, into representations of his proposed group.

In this manner the otherwise mysterious Gell-Mann-Nishijima

formula—which relates charge, hypercharge, and isospin—had

a natural explanation. It later turned out that Schwinger’s

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

16 B IOGRAPHICAL MEMOIRS

later to become an integral part of today’s successful electroweak

theory. The known leptons—in Schwinger’s perversely

original interpretation—were to form a weak isospin

triplet: {ì+, í, e−}. An immediate consequence of this notion

was the selection rule forbidding ì→e + ã and the obligatory

distinction between neutrinos associated with electrons

and muons. “Is there a family of bosons that realizes the

T=1 symmetry of [the lepton symmetry group]?” 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.

Schwinger’s 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 “it can be of value if it provides a

convenient frame of reference in seeking a more coherent

account of natural phenomena.” 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 Schwinger’s nonperturbative

field theoretic concepts and methods for the vacuum

state to material systems in equilibrium at nonvanishing densities

and temperatures, and a 1961 paper, camouflaged by the

title “Brownian Motion of a Quantum Oscillator” 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, Schwinger’s “two-time” approach is now

j u l i a n s chwi n g e r 17

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 “Schwinger terms.” He followed it in

papers directed toward the gravitational field with a study of

the conditions imposed by consistency on stress tensor commutation

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 theory’s 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 experiment—from 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 “anabatic” (going

up) phenomenological source theory was, he maintained,

immensely different from “the speculative approach of

18 B IOGRAPHICAL MEMOIRS

trickle-down” field theory. So too were its predictive powers.

He espoused this contrarian position steadfastly.

During the 1960s, Schwinger’s 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 California,

with students, new collaborators, and longtime friends,

Schwinger continued working on source theory (“source”

appears in the title of more than 15 publications) and contributing

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 Schwinger’s last papers is a 1993 talk titled “The

Greening of Quantum Field Theory: George and I, Lecture

at Nottingham, July 14, 1993.” It contains the count of references

to Green in Discontinuities in Waveguides mentioned

earlier and a recital of a multitude of the linkages with

George Green of Schwinger’s research on field and particle

theory, statistical mechanics, through to work on the Casimir

effect and sonoluminescence. Although Schwinger’s genius

was widely recognized immediately, and Green’s very slowly.

Schwinger concludes his talk by answering the question,

j u l i a n s chwi n g e r 19

“What then shall we say about George Green?” with “He is,

in a manner of speaking, alive, well, and living among us.”

That, too, can be said for Schwinger.

Schwinger’s 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 Schwinger’s professional offspring

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 Schwinger’s 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 considerate

and willing to do his best to provide scientific advice

when he thought help was needed. His insight and suggestions

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 timeconsuming

political maneuvering; to understand, extend,

unify, and generalize; and to reveal the hidden beauty of

nature. Walter Kohn spoke for all of Schwinger’s students

in saying,

20 B IOGRAPHICAL MEMOIRS

We carried away the self-admonition to try and measure up to his high standards;

to dig for the essential; to pay attention to the experimental facts;

to try to say something precise and operationally meaningful, even if—as

is usual—one cannot calculate everything a priori; not to be satisfied until

ideas have been embedded in a coherent, logical and aesthetically satisfying

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.

j u l i a n s chwi n g e r 21

SELECTED BIBLIOGRAPHY

1935

With O. Halpern. On the polarization of electrons by double scattering.

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 hydrogen.

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.

22 B IOGRAPHICAL 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 Green’s 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 Green’s 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.

j u l i a n s chwi n g e r 23

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

Einstein’s Legacy: The Unity of Space and Time. New York: W. H. Freeman

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.

    本站是提供个人知识管理的网络存储空间,所有内容均由用户发布,不代表本站观点。请注意甄别内容中的联系方式、诱导购买等信息,谨防诈骗。如发现有害或侵权内容,请点击一键举报。
    转藏 分享 献花(0

    0条评论

    发表

    请遵守用户 评论公约

    类似文章 更多