Curiculum Vitae
Other Writings
Book reviews
from the
Dutch Mathematical
Book reviews
from the journal
Acta Applicandae

Book review

Author(s) Sterman, George
Title An Introduction to Quantum Field Theory
Publisher Cambridge University Press
Year of publication 1993
Reviewed by Paul A. Blaga

There is no doubt that quantum field theory (here after QFT) is one of the most important parts of contemporary theoretical physics. It is quite impossible to understand completely the physics of elementary particles without a good knowledge of QFT. It is for these reasons that the publication of a new (and good, as argued below) book of QFT is an enjoyable event. As the author himself writes in the introduction, the aim of this book is to provide a "self-contained introduction to relativistic QFT and its applications to high-energy scattering".

The book contains a great amount of material, so that it would not be possible to describe all of its contents. Instead, I'll try to provide at least an outline of them. The book is divided in four parts, mainly for pedagogical reasons. The first part is devoted to scalar fields, the author wishing to illustrate the basic methods of QFT on this most simple case. There are presented here the essential methods and notions, relying on group symmetries and path integrals, Feynman rules, as well as scattering and cross-section for scalar fields a.o.

In the second part there are considered fields with spin, more realistic from the physical point of view. Two chapters are dealing with the space-time symmetries and canonical quantization of these theories, with an introduction to unitary representations of Poincaré group, as related to quantization. The remaining two chapters develop the path integral theory for fermion and gauge fields and a description of the lowest order gauge theories, as applied to quantum electrodynamics (QED) and quantum cromodynamics (QCD). It is supposed that after the reading of this first half of the book, the student is already able to understand the standard model and some of its experimental consequences.

The second half of the book (also composed of two parts) is dealing with more advanced topics, closer to the research interests of the author. Part III is concerned with renormalization. Nevertheless, the first chapter of this part (ninth of the book) includes, also, topics as Wick rotation, dimensional regularization, unitarity a.o. After that the author presents an introduction to renormalization theory (including the renormalization group) and the relationships between renormalization and the unitarity of gauge theories, as applied to QED and QCD. There is, also, a description of the axial anomaly, as an illustration of the relation between Classical and quantum symmetries. The Part IV undertake an extensive discussion of the nature of perturbative cross-section. Among the topics touched in this part, I should remind: one-loop corrections in QED, infrared divergences and infrared safety, analytic structure of Feynman diagrams, Kinoshita-Lee-Nauenberg theorem, deeply inelastic scattering a.o. (the list is not, by any means, exhaustive). The book concludes with several appendices (7) dealing, for instance, with: The Goldstone Theorem, cross-sections and Feynman rules, the standard model a.o.

Let me now emphasize some of the strength of the book. First of all, the presentation is systematic, pedagogic and starts from the very first principles, paying attention not only to theoretical concepts, but, also, to experimental applications. The applications chosen are essential for all students interested in elementary particle physics. Moreover, the mathematical parts of the book are excellent written and self-contained (at least to some extent). The book doesn't include anything about supersymmetry or about the relation with gravity, but it wouldn't be possible to treat all these problems in detail, in a book of reasonable size. The book can be used as a textbook for graduate courses in QFT, or as a reference book. There are, of course, excellent alternatives (e.g. Itzykson and Zuber - Quantum Field Theory, McGraw-Hill, 1980), but this book is, in many respects, unique and is to be recommended to graduate students, experts in other fields wishing to learn QFT, and even to experts, especially if they are interested in high-energy scattering, the author himself being an expert in this field.

The book has a detailed index and an extended list of references. It is produced by using a processor from the TeX family.