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.