by Jagdish Mehra and Kimball Milton, Oxford, ISBN 0198506589.
Climbing the Mountain is the first full-length biography of Julian Schwinger. There is also a companion volume, A QuantumLegacy (World Scientific), edited by Milton, which complements a previous collection of Schwinger papers edited by C Fronsdal, M Flato and K Milton. An earlier volume, Julian Schwinger, the Physicist, the Teacher and the Man (World Scientific), is a compilation of tributes delivered at various memorial symposia by friends and former students and edited by Jack Ng. There is also a third volume, QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga by S S Schweber (Princeton University Press).
This biography describes Julian Schwinger’s life as well as his work. The treatment of his scientific work is scholarly and well done. The challenge faced by this book is well stated in the preface: “Julian Schwinger was one of the most important and influential scientists of the 20th century…yet even among physicists recognition of his fundamental contributions remains limited.” This is all the more remarkable since Schwinger had more than 70 students, many of whom became very distinguished, including three Nobel laureates.
Climbing the Mountain confronts this challenge by a very extensive discussion of Schwinger’s manifold contributions. On the other hand one may still ask how it is possible that C N Yang can recall that when he entered the University of Chicago in 1946 as a graduate student, Julian Schwinger was already a legend (even before he had published his monumental papers on quantum electrodynamics), while in the year 2000 so little is known about Schwinger and so much is known about Feynman.
The answer lies partly in the personalities of the two men, but also in the beautifully simple and powerful diagrammatic notation invented by Feynman (which, in Schwinger’s words, “like the silicon chip, would bring computation to the masses”) and finally his separation from the mainstream in his later years.
The most important part of the Schwinger-Feynman story is summarized by the Michigan Summer Schools of 1948 and 1949. In 1948 Schwinger first described his breakthrough in QED to a wider audience, including Dyson, Kroll, Lee and Yang. It was thenthat Dyson wrote home that in a few months we shall have forgotten what pre-Schwinger physics was like.
In the following 1949 Michigan lectures, Feynman described his version of QED, but at that time he was unable to deal with vacuum polarization and it was not generally clear how much he had been able to accomplish.
By contrast, Schwinger had presented an essentially complete package: a manifestly covariant theory with which he had calculated in lowest order all the previously inaccessible consequences of QED. He had not only climbed the mountain but, more importantly, had shown that it could be climbed. Shorter routes were subsequently found. In the third year of the Michigan series, Dyson lectured and showed that the Schwinger theory and the completed Feynman theory were equivalent. This history, as well as the parallel work of Tomonaga, is well described in this book.
The Schwinger theory of 1948, while adequate for its original purpose, was, like every first invention, relatively crude and could not easily be pushed to higher order. Therefore during the 1950s he developed increasingly powerful calculational techniques. To this period belong the Schwinger action principle and the extensive use of Green’s functions and functional techniques that are now part of the standard literature.
During the 1960s Schwinger began a total reconstruction of quantum field theory that he named source theory. Here he was attempting to replace the operator field theory, to which he had contributed so much, by a philosophy and methodology that eliminated all infinite quantities. He did in fact succeed in constructing an infinity-free formalism that was also receptive to new experimental information and new theoretical ideas. It was not simply a programme: Schwinger and his UCLA source theory group, K Milton and colleagues, showed that it was a very effective calculational tool. Source theory has not until now found extensive use in the general theoretical community, although it has elements in common with S Weinberg’s use of phenomenological Lagrangians. Schwinger’s determination to pursue this work for about 10 years led to his partial eclipse. Milton is obviously well qualified to review this period.
One of the more interesting chapters is entitled “Electroweak Unification and Foreshadowing of the Standard Model”. Not so well known is Schwinger’s role in the development of the electroweak theory. In 1941 he made the amazingly prescient remark that if the significant mass scale for nuclear beta-decay were of the order of several tens of nuclear masses, then there would be the possibility of an intermediate vector theory with a coupling of the order of alpha. The theory suggested by this numerology was essentially realized in 1957 in his beautiful paper “A Theory of the Fundamental Interactions” (1957 Ann. Phys.2 407). Schwinger comments on this paper (82) in the selected papers (edited by Flato et al.):
“A speculative paper that was remarkably on target: VA weak interaction, two neutrinos, charged intermediate vector meson, dynamical unification of weak and electromagnetic interactions, scale invariance, chiral transformations, mass generation through vacuum expectation value of scalar field. Concerning the idea of unifying the weak and electromagnetic interactions, Rabi once reported to me: ‘They hate it’.”
However, he was convinced and proposed a similar model to his student, Glashow. Thanks to the efforts of Glashow, Weinberg, Salam and ‘t Hooft the standard electroweak SU(2) x U(1) theory, bearing enormous similarity to Schwinger’s paper of 1957, was born. The 1957 paper might well have led directly to the standard electroweak theory if it had not become bogged down in the infamous morass of 13 flawed experiments that seemed to imply that the beta-interaction was not VA.
Schwinger’s independence of the mainstream is discussed in this biography and by many others including Schweber. It is said that he didn’t like “conversational physics” but that meant only that he didn’t like conversations unless they interested him. In fact he was quite open to new ideas.
The more accurate view is that he was simply an independent thinker who guarded his time and set his own goals, toward which he worked intensely and constantly. Much of his work he made no effort to publish. For some of his work, like the Bethe-Salpeter equation and the TCP theorem, he received no recognition.
It is arguable that the creativity of an original mind such as Schwinger’s or Dirac’s would have been enhanced by more interaction with others in later years. In Schwinger’s case, in spite of the undeniable handicaps of isolation, the following assessment appears in the Festschrift published on the occasion of his 60th birthday:
“His work during the 44 years preceding his 60th birthday extends to almost every frontier of modern theoretical physics. He has made far-reaching contributions to nuclear, particle and atomic physics, to statistical mechanics, to classical electrodynamics and to general relativity. Many of the mathematical techniques he developed can be found in every theorist’s arsenal…He is one of the prophets and pioneers in the uses of gauge theories…Schwinger’s influence, however, extends beyond his papers and books. His course lectures and their derivatives constitute the substance of graduate physics courses throughout the world, and in addition to directing about 70 doctoral theses, he is now the ancestor of at least four generations of physicists…The influence of Julian Schwinger on the physics of his time has been profound.”
