ÌÇÐÄVlog

The standard model of particle physics appears to provide an excellent description of the interactions of the elementary constituents of matter, the quarks and leptons. Much experimental effort is being devoted to precision tests of this theory, and to searches of "physics beyond the standard model". So far the standard model has passed these tests remarkably well.

Indeed, much to our frustration, there is no direct evidence yet for new physics, which might give clues towards an understanding of the many fundamental questions not explained by the standard model (such as why the charge of the electron is equal and opposite to that of the proton or why the quarks and leptons appear in three families). Within the standard model the properties of the strong and weak nuclear forces, and of the electromagnetic interactions, are described by quantum field theories with a local gauge symmetry. In addition, many attempts to extend the standard model, for example by constructing "grand unified theories'' of the strong, weak and electromagnetic interactions, are also based on (non-Abelian) gauge theories. Thus quantum field theory is the main theoretical framework physicists use to describe the properties and interactions of elementary particles. The Quantum Theory of Fields, by Steven Weinberg, is a comprehensive, two-volume text on the subject.

The first volume was published last year, and was subtitled Foundations. The second volume, subtitled Modern Applications, deals primarily with the structure, properties and implications of gauge field theories. Weinberg has made many important contributions to the development of quantum field theory, and shared the 1979 Nobel prize for physics with Sheldon Glashow and Abdus Salam "for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including inter alia the prediction of the weak neutral current". He is also a renowned expositor: his previous books include The First Three Minutes, in which he skilfully explains the physics of the early universe to the general reader, and the classic textbook Gravitation and Cosmology, from which many of us learned these subjects. It is therefore not surprising that The Quantum Theory of Fields offers a clear presentation of the subject, explaining the underlying concepts in much depth and in an accessible style. I expect that these volumes will become the first source we turn to when trying to answer the challenging questions asked by bright postgraduates when they first encounter quantum field theory. Although quantum field theory is also important in other areas of physics, this book is written primarily for theoretical particle physicists.

There are sections on critical phenomena and superconductivity, but these are "somewhat out of the book's main line of development and may be omitted in a first reading". The reader is assumed to have mastered the contents of the first volume, and hence to be familiar with topics such as path integrals, the evaluation of one-loop diagrams in quantum electrodynamics and general renormalisation theory.

The main emphasis in the second volume is on explaining the concepts and ideas of gauge theories, rather than on equipping the potential researcher with all the techniques necessary to perform state-of-the-art calculations. This is illustrated, for example, by the absence of a compendium, traditionally found in textbooks on quantum field theory, containing the Feynman rules for different field theories and other identities useful in practical calculations.

The techniques are relatively easy to master, however, and the student who has studied this volume will be admirably prepared to read the more specialised texts and recent research literature before beginning his or her research project. But I cannot help reflecting with some regret that, in the United Kingdom at least, we do not allow most of our research students the two years the author estimates is required to study most of the material in the two volumes.

The second volume starts with a general description of non-Abelian gauge theories. The quantisation and renormalisation of these theories is discussed in detail, stressing the role of the BRST symmetries in enormously simplifying the procedures. These opening three chapters are challenging, with little respite from the formalism, but are rewarding.

The author carefully introduces the important concepts of the quantum effective action and potential, and explains very clearly their interpretation in terms of energy and energy density. It is also very pleasing to find a detailed description of the background field gauge, together with an example demonstrating its value. Quantum chromodynamics (QCD) is the field theory of the strong nuclear force, describing, at the fundamental level, the interactions between quarks and gluons. QCD has the property of "asymptotic freedom", which implies that when the quarks and gluons interact at very short distances (distance smaller than about 1/10th fermi or 10-16metre), the strength of the interaction decreases, and we can use perturbation theory to calculate predictions for physical processes.

Much of today's research in elementary particle physics relies on this fact to give us control over the strong interaction effects. Two chapters of this book are devoted to "renormalisation group methods" and "operator product expansions", in which, as part of a more general discussion, the theoretical background to the concept of asymptotic freedom and its applications are described in detail. These chapters also contain an introduction to some of the tools that are required to perform perturbative calculations in QCD, for instance the minimal subtraction and related renormalisation schemes are briefly described and the use of the operator product expansion and renormalisation group in predicting the distributions of quarks and gluons inside the proton and other elementary particles is explained. Spontaneously broken symmetries, in which the symmetries of the theory are not realised as symmetry transformations of the physical states, play a fundamental role in particle physics.

The classic example of a spontaneously broken (approximate) global symmetry is the chiral symmetry of QCD, which implies that the pion is considerably lighter than other strongly interacting particles. Weinberg has been one of the principal contributors to the development of our understanding of this subject, and the chapter on spontaneously broken global symmetries provides a particularly valuable and thorough description of the general features, from the appearance of Goldstone bosons to nonlinear realisations and the construction of effective field theories of pions and nucleons.

The most important unsolved problem within the standard model of particle physics is our ignorance of the details of the mechanism which generates particle masses. It is believed that mass generation occurs through the Higgs mechanism, based on the spontaneous breakdown of local gauge symmetries, but for us to understand exactly how this is realised in nature, requires further experimental information, perhaps from the next generation of particle accelerators.

The Higgs mechanism is described in detail, and is followed by a description of the electroweak theory and a discussion of grand unified theories. The final two chapters deal with two important topics in considerably more depth than is usually found in general textbooks on quantum field theory. These chapters will be much appreciated. The first of these is a detailed description of "anomalies", the breaking of symmetries present in the classical theories by quantum corrections.

In the last chapter the author provides an excellent minireview of extended objects in quantum field theory, offering an introduction to the concepts in topology which he uses, and briefly (perhaps too briefly) explaining their physical significance in, for example, the U(1) and strong CP problems. I have no doubt that The Quantum Theory of Fields will soon be found on the bookshelves of most particle theorists, and that it will be one of the main sources used in the preparation of lectures on the subject for post-graduate students. The two volumes will provide an important resource for researchers, and hopefully the exciting new developments in field theory based on duality and supersymmetry will eventually form the material of the third volume hinted at by the author in his preface.

C. T. C. Sachrajda is professor of physics, University of Southampton.