Product Description

This book is a clear and comprehensive introduction to quantum field theory, one that develops the subject systematically from its beginnings. The book builds on calculation techniques toward an explanation of the physics of renormalization.

Product Details

• Amazon Sales Rank: #94341 in Books
• Published on: 1995-10-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 864 pages

About the Author

Customer Reviews

Good introduction to Feynman diagrams
I worked through the most of this book in explicit detail (the only way to get the full benefit, in my humble opinion), and, while it was very good at teaching the methods for deriving and computing Feynman diagrams, it often sacrifices pedagogy for explicit calculation. For instance, while there is a brief discussion of representations of the Lorentz group, the book gives no indication of how to construct and work with fields of higher spin. Also, I found their discussion of the LSZ reduction formulae rather impenetrable. (Their discussion of BRST symmetry, in contrast, is very readable and easily understood.) So, while I would recommend this book to anyone who wants to learn to do calculations in quantum field theory, it is imperative that they supplement this book with other sources that treat important topics, like the CPT theorem, general representation theory, and non-perturbative phenomena (which are barely mentioned here), in detail. (Also, there are a rather large number of unfortunate typos in the first edition...)

A great book; better when supplemented
This is a difficult book to review. That a detailed study of several textbooks is needed for a thorough introduction to QFT is a well-known maxim among students of the subject. Every QFT text excels in some areas and struggles in others, and Peskin and Schroeder's book (P&S) is no exception. P&S chooses to emphasize performing calculations in the Standard Model (SM), and the chapters pertaining to this topic are excellent. Chapters 5 and 6, covering tree and one-loop calculations in QED, are invaluable, as are chapters 20 and 21, which detail the electroweak theory.

Several of the formal aspects of QFT are shunted in P&S, as must something be neglected in every QFT text that is stable against gravitational collapse. The general representation theory of the Lorentz group is the most glaring omission in P&S. Chapter 1 of Ramond's "Field Theory: A Modern Primer" treats this topic quite well. The LSZ reduction formulae are derived and discussed more clearly in Pokorski's "Gauge Field Theories", as are BRST symmetry and free field theory. For those interested in undertaking detailed phenomenological studies of the SM or some extension thereof, Vernon Barger's "Collider Physics" is also recommended.

Despite its shortcomings, P&S remains the best QFT reference currently available. It's the book I turn to first when confronted in research papers with field theoretic puzzle that I just can't crack. If you buy only one QFT text, buy P&S.

Promotes physical insight and understanding...not formalism
The authors give an excellent overview of the physical concepts and computational aspects of quantum field theory. They stress the situation behind the subject, and endeavor to remain as concrete as possible. Abstract mathematical constructions are left to more advanced texts in quantum field theory. The authors characterize their book as an updating of the two volume set of Bjorken and Drell.

The main emphasis of the book is on quantum electrodynamics (QED), the most successful of quantum field theories. The representation and analysis of the physical processes of QED is done via Feynman diagrams, with electron-positron annihilation leading off the discussion. Recognizing that the exact expression for the amplitude of this process is not known, perturbation theory is used to give an approximate representation for it via an infinite series with each term involving successively higher powers of the strength of the coupling between the electrons and photons (i.e. the charge). Each term is represented as a Feynman diagram. This is followed by a discussion of the quantum field theory of the Klein-Gordon field. The authors give one of the best explanations in the literature of why one must deal with the quantization of fields and not particles, the most important one being causality. Canoncial quantization is employed and the Feynman propagator for the Klein-Gordon field is derived. The Dirac field is also quantized using the canonical formalism. The authors show that Klein-Gordon fields obey Bose-Einstein statistics and Dirac fields obey Fermi-Dirac statistics. The all-important Wick's theorem is proven and higher-order Feynman diagrams are discussed. Most importantly, the authors show how to connect these results to experiment via the calculation of cross sections and decay rates. This entails the computation of the S-matrix elements from Feynman diagrams. The authors are very detailed in their elucication of the discussion, and those who have done these calculations know that it is great fun to do so. In addition, these "bread-and-butter" calculations give quantum field theory its ultimate justification in the modern particle accelerator. The discussion on radiative corrections is especially well-written, particularly the section on infrared divergences.

The authors do not entirely neglect the more formal aspects behind quantum field theory, and spend some time discussion renormalization and the amazing Ward-Takahashi identity. This important identity gives one further confidence in the consistency of QED in that is shows that timelike and longitudinal photons can be neglected in the actual calculations. The process of renormalization has been viewed with suspicion by mathematicians, but it has been given a firmer foundation recently using, interestingly, mostly 19th century mathematics. The authors discuss functional methods, and give an example of its use by calculating the photon propagotor. Viewing this as a constrained problem because of gauge invariance they use the Faddeev-Popov gauge fixing condition to obtain the correct results. In addition, they derive the important Schwinger-Dyson equations for QED using functional methods.

Effective field theories are also introduced in the book, with an explicit calculation of the effective action. The authors show the important connection between continuous symmetries and the existence of massless particles (Goldstone's theorem). Their discussion of the renormalization group is very understandable, and they motivate the subject well, by asking why the loop integrals over virtual-particle momenta are always dominated by values on the order of the finite external momenta.

Non-Abelian gauge theories are given a thorough treatment and Wilson loops are introduced as a comparator between gauge transformations at different spacetime points. The quantization of these theories is again done by viewing the quantization problem as a constrained problem, and the famous "Lagrange multlipiers", the Faddeev-Popov ghosts, are introduced. The authors show in detail how their introduction allows the correct Feynman rules to be produced, by showing that the unphysical timelike and longitudinal polarization states of the gauge bosons are cancelled by these fields. The BRST symmetry is discussed as a formal device to to this cancellation. The omit though how the Ward identities are derived from BRST symmetry.

The authors give the best explanation in the literature of asymptotic freedom by showing the effect of vacuum fluctuations on the Coulomb field of a SU(2) gauge theory.

The important operator product expansion is treated in the context of the Callan-Symanzik equation in quantum chromodynamics. It is applied to the deep inelastic scattering and electron-positron annihilation. Dispersion relations make their appearance here.

The authors also discuss anomalies and motivate the subject by analyzing the axial current in two-dimensional massless QED. The axial current is shown not to be conserved in the presence of an electromagnetic field, and they conclude that gauge invariance and conservation of axial currents in this theory cannot both be simultaneously satisfied. This is generalized to axial currents in four dimensions and the authors derive the famous Adler-Bell-Jackiw anomalies. The implications of anomalies for gauge theories are discussed along with observable consequencies.

The (mysterious) Higgs mechanism is also discussed and compared to the situation in superconductivity. To view it in terms of superconductivity I think gives it the most plausible and intuitive justification. Understanding the Higgs mechanism is a usual stumbling-block for newcomers to gauge theories, and the authors do a fair job here. The quantization of spontaneously broken gauge theories is then carried out, with emphasis on the Goldstone boson equivalence theorem. A brief discussion of the future of quantum field theory ends the book.

When reading this book, and others on quantum field theory, I am always amazed at the degree to which it works, and its elegance, despite the fact that it really is a collection of ad hoc strategies and sophisticated guesswork. One gets the impression that there is something profound behind the scenes, still waiting to be discovered, and which will be able to shed light on the major unsolved problem of quantum field theory: the existence of a bound state.