An Introduction to Quantum Field Theory

Amazon.com Review:

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.