Foundations of Physics, Vol. 22, No. 4, 1992
Book Review
Relativistic Quantum Mechanics of Leptons and Fields. By Walter T. Grandy, Jr. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, x + 438 pp., $99.00 (hardcover).
Twenty years ago in graduate school I was fortunate to come across Grandy's attractively slender Introduction to Electrodynamics and Radiation (Academic Press, 1970). More recently I have heard praises of his heftier Foundations of Statistical Mechanics (Reidel, 1987), but unfortunately I have not yet found time to study these volumes. I saw the opportunity to review Grandy's latest book as just the excuse I needed to review some old things and learn some new ones, and I expected from the author a scholarly and unpretentious presentation. I am happy to report that my expectations were fully met. Relativistic Quantum Mechanics of Leptons and Fields is mainly about the theory and application of the single-particle Dirac equation. It is written as a textbook, with end-of-chapter problems, but, as the author acknowledges, it has "some flavor of a monograph." I found it to be not only a fairly thorough technical account of the classical field theory of ~b, but, also a good physical discussion of this and other topics. The first chapter, "Nonrelativistic Quantum Mechanics," is a formal, concise, and logically appealing review of Schr6dinger's equation, symmetries, spinors, minimal coupling of a point charge with spin to the electromagnetic field, and the two-body problem. The author's description of it as "a somewhat sophisticated review of nonrelativistic quantum mechanics for the already-knowledgeable" is very accurate. The next several chapters focus on the single-particle Dirac equation, electromagnetic interactions, and propagator theory, with an interlude on "Neutral Fermions and Bosons." The material here is predictable and standard, as of course it must be. However, two things enlivened these chapters for me, and reinforced my opinion that there are still things to be 631 0015-9018/92/0400-0631506.50/00 1992 Plenum Publishing Corporation
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learned after all these years. First, the cited literature includes not only the old classics but also recent (up to the late 1980s) research and pedagogical papers. Many of these I had not seen, and the fact that titles are provided in the references enticed me on several occasions to look up some of the recent papers--thereby delaying this review. Second, the author is careful to spell out some underlying assumptions (e.g., the notion of the pure point electron) that are typically lost in the formalism of the older books. Obviously these are very useful features for students approaching relativistic quantum theory for only the first, second, or third time. Chapter 7, "The Quantum Theory of Radiation," and a lengthy Appendix, "Classical Theory of the Electron," are in large part independent of the rest of the book, and both could be useful supplements to standard graduate courses in quantum mechanics and electromagnetism. Both, in fact, have the character of review articles. Chapter 7 appears to me to be a very well-balanced critique of QED and alternative, semiclassicat theories. Unlike authors of too many other advanced texts, who seem to find more comfact in formalism than in questions of physics, Grandy addresses the question of the "reality" of the vacuum field in some detail. With regard to renormalization, one clearly senses the author's dissatisfaction, but he is careful to point out that the electron's mass and charge would have to be renormalized, logically, even if their calculated corrections were both finite. He reminds us repeatedly that we have nothing better than renormalization, and that renormalization produces remarkably accurate agreement with experiment. The Appendix, which focuses largely on radiation reaction, seems to me to be among the clearest and most exhaustive modern treatments available. Grandy makes it clear that the classical, nonrelativistic theory of an extended charge is fully self-consistent. The corresponding quantum theory is only briefly touched upon. (At the time of this writing I have recently discovered, through Dresden's biography of Kramers, that van Kampen's thesis provided a consistent nonrelativistic quantum theory of the extended electron.) Chapter 8, "The two-Body Problem," gives more details than I was interested in following in a general first reading of the book, whereas the following chapter, "Dirac Scattering Theory," gives a nice review of nonrelativistic single-channel scattering formalism with only enough details of the relativistic theory to put a beginner on the right track. The final chapter, "Quantum Etectrodynamics," is a general overview of the quantization of the Maxwell and Dirac fields, and gives a few examples, concluding with a discussion of vacuum polarization in terms of the photon propagator. One goal of Relativistic Quantum Mechanics of Leptons and Fields is to show just how far one can get with the classical field theory of leptons
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and fields, I believe that Grandy has fully accomplished that goal, and has done this with a refreshing emphasis on what J, J. Sakurai called "Physics with a capital P?' Peter. W. Mitonni Theoretical Division, Mail Stop B-268 Los Alamos National Laboratory Los Alamas, New Mexico 87545
