The Feel of the Atelier
Chris Quigg

The Quantum Theory of Fields: Vol. 2, Modern Applications. By Steven Weinberg. xxi+489 pp. Cambridge: Cambridge University Press.

Some time ago, I visited a harpsichord-maker in his workshop. The artisan showed me his materials, explained the various stages in the construction of harpsichords, then treated me to a recording of Igor Kipnis playing the Fandango on one of his instruments. But the object he took the greatest pleasure in showing me was not a finished harpsichord, but a block plane—clean, precise, and utterly apt—that he had built in order to sculpt soundboards of surpassing beauty and eloquence. This maker of wonderful instruments was also a maker of wonderful tools.

Reading volume 2 of The Quantum Theory of Fields took me back to the harpsichord-maker’s workshop, because Steven Weinberg is one of our most gifted makers of theoretical tools as well as a virtuoso in their use. His new book conveys both the satisfaction of understanding nature and the feel of the atelier, for the “modern applications” of its subtitle include both the derivation of physical consequences and the development of new tools for understanding and applying field theory itself.

Quantum field theory is the theory of matter and its interactions that grew out of efforts begun in the late 1920s to join quantum mechanics and relativity. Thanks in considerable measure to its successes over the past quarter-century, quantum field theory has become the preferred conceptual and mathematical framework for approaching many of the fundamental problems of physics. Indeed, it is the resemblance among the field theories of the strong, weak, and electromagnetic interactions that inspires the hope for a unified theory of them all.

Two great themes are at the heart of Modern Applications: the rôle of symmetry in determining the fundamental interactions and the concept of symmetries that are hidden at low energies. Weinberg’s treatment of non-Abelian gauge theories—specifically quantum chromodynamics, the theory of strong interactions among quarks—is notable for an explicit calculation of the quantum corrections that make the coupling constant of the theory depend on the energy scale. This illuminates the remarkable feature of “asymptotic freedom,” whereby the strong interactions become feeble—and susceptible to analysis by perturbation theory—at high energies. This leads in turn to a clear and thorough presentation of the varieties of asymptotic behavior for a field theory, using the methods of the renormalization group.

Hidden symmetries are treated in two masterly chapters devoted to global and local symmetries. The discussion of the pion as an avatar of chiral symmetry breaking integrates the fruitful current-algebra approach of the 1960s with our modern understanding based on quantum chromodynamics. A highlight of the chapter on local symmetries is a rich discussion of superconductivity as a consequence of the spontaneous breaking of electromagnetic gauge symmetry. The superconducting phase transition is our model for hiding the electroweak symmetry, and a detailed examination using the tools of modern field theory is rewarding.

As quantum field theory and gauge theories have become more central to our study of physics at very short distances, or very high energies, we have changed our attitude about the theories themselves. We no longer demand that our theories make sense up to arbitrarily high energies, but regard them as effective theories that are appropriate to describe the important physics in various energy regimes. In many instances, effective field theories provide the most convenient tool for working out the consequences of symmetries and the general principles underlying quantum field theory. Among the many tools Weinberg presents, he shows effective field theories with particular pleasure.

The Quantum Theory of Fields: Modern Applications is a splendid book, with abundant useful references to the original literature. It is a very interesting read from cover to cover, for the wholeness Weinberg’s personal perspective gives to quantum field theory and particle physics. An author index and a well-chosen subject index make Modern Applications a valuable reference book.

For a highly motivated and superbly prepared student, The Quantum Theory of Fields: Modern Applications could serve as a textbook, with or without its companion volume. The ideas of each chapter are elaborated by several thought-provoking problems. I will recommend it to students who have completed a first course in field theory, and hope that many of my colleagues will read it as well. Weinberg leads us to a frontier rich in possibilities. This is an optimistic book, written with much respect for ideas and nature—and for tools.

Published in Science 275, 938 (1997).