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Quantum Leap

Paul Frampton

Quantum Field Theory, Second Edition. Lewis Ryder. 512 pp. Cambridge University Press, 1996. $29.95.

Quantum Theory of Fields. Steven Weinberg. Volume 1, Foundations. 500 pp. Cambridge University Press, 1995. $54.95. Volume 2, Modern Applications. 500 pp. Cambridge University Press, 1996. $49.95.

The publication of a second edition of Lewis Ryder's Quantum Field Theory 11 years following the original edition of 1985 is very welcome. This book has proved popular to beginning graduate students and senior undergraduates who want a gentle introduction to this complicated subject. The principal change in the second edition is the addition of a chapter on supersymmetry. Although there is no experimental evidence for supersymmetry, the formalism is elegant, and there are enough journal papers and seminars on supersymmetry that students benefit from being taught this material. On established topics, the presentation of quantization of field theory is particularly careful and includes both canonical and path-integral methods. As expected, the treatment of renormalization is more descriptive than rigorous; there is also a brief chapter on nonperturbative techniques. The great virtue of Ryder's book is its accessibility to students who seek a first understanding of quantum field theory including basic concepts of quantization. This book is now a staple in the physics canon.

At the other end of a shelf of books on quantum field theory should be placed the Quantum Theory of Fields, Volumes 1 and 2, by Steven Weinberg. These form an advanced 1,000-page treatise intended both as a reference work for researchers and as a textbook appropriate for graduate students. Its use as a textbook is encouraged by Weinberg's inclusion of problems at the ends of the chapters. The appearance of this book has been long anticipated because of the author's distinction as a Nobel prizewinner for the electroweak theory. Also, Weinberg has previously written a successful textbook entitled Gravitation and Cosmology (1972). The present two-volume work is impressively produced with an attractive format and dustcovers and with a reassuringly low density of typographical errors for such a lengthy work.

The first half of Volume 1 is lengthy and detailed on the foundations, including analysis of the Lorentz group and its representations, S-Matrix theory, and cluster decomposition. Fields are then quantized both in the canonical formalism and (with a view to Volume 2) by path integrals. Chapter 11 is a full treatment of the one-loop graphs in quantum electro-dynamics with the interesting addition of the leading two-loop contribution to the muon magnetic moment. Chapter 12 introduces the general theory of renormalization. The modern viewpoint taken is to emphasize effective Lagrangians rather than the renormalizability criterion by which the electroweak theory was identified almost 30 years ago. Of course, the use of effective theories is more general and leads one to expect renormalizability of the effective theory by arguments based simply on the different energy scales at which physics may appear. Explanations are characteristically clear and precise, and the style is very authoritative.

As graduate textbooks, Weinberg's volumes are more suitable as supplemental reading than as the required text. This is partly because the style is detached and scholarly and partly because the all-important non-Abelian gauge theories make their appearance only after 600 pages, at the beginning of Volume 2. One possibility is to use just Volume 2 as the basis of a graduate course leading to particle theory research. In Volume 1, there are some idiosyncrasies. For example, in Chapter 6 Feynman rules are derived with the unusual generality of arbitrary spin. As a result, the notation becomes very sophisticated and distracting for students. In Chapter 14, the Lamb shift is calculated without the simplification of dimensional regularization.

Volume 2 is on the "modern applications" and naturally centers on non-Abelian gauge theory, starting with the quantization by path integrals, BRST symmetry and renormalization. Perhaps my favorite is Chapter 18, a presentation of the renormalization group including the implications that asymptotic freedom may be essential to the consistency of field theory at all energy scales, as well as to the correct relation between a discretized space-time lattice version and its continuum limit. It is fascinating to read Weinberg on the relationship of Wilson to Gell-Mann and Low! The next two chapters are mainly concerned with topics in quantum chromodynamics for strong interactions. Chapter 21 discusses spontaneous breaking of gauge symmetry, the Higgs mechanism and hence the successful electroweak theory. The work ends with a chapters on anomalies and nonperturbative effects.

As reference works these volumes are an absolutely essential addition to the bookshelf of any practicing field theorist. They provide a treasure trove of information and bibliography. To summarize, the Ryder is a welcome second edition of a popular introductory text, and the Weinberg work is the long-awaited authoritative modern treatise on the same subject and a landmark in the history of quantum field theory. They are a must-buy for every university physics library.—Paul H. Frampton, Physics, University of North Carolina at Chapel Hill

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