Synopses & Reviews
As a fundamental branch of theoretical physics, quantum field theory has led, in the last 20 years, to spectacular progress in our understanding of phase transitions and elementary particles. This textbook emphasizes the underlying unity of the concepts and methods used in both domains, and presents in clear language topics such as the perturbative expansion, Feynman diagrams, renormalization, and the renormalization group. It contains detailed applications of critical phenomena to condensed matter physics, such as the calculation of critical exponents and a discussion of the XY model. Applications to particle physics include quantum electrodynamics and chromodynamics, electroweak interactions, and lattice gauge theories. The book is based on courses given over several years on statistical mechanics and field theory, and is written at graduate level. It attempts to guide the reader through a somewhat difficult and sometimes intricate subject in as clear a manner as possible, leading to a level of understanding where more advanced textbooks and research articles will be accessible. The only textbook covering the subject at this level, the work is thus an ideal guide for graduate and postgraduate students in physics, researchers in quantum and statistical field theory, and those from other fields of physics seeking an introduction to quantum field theory. A large number of problems are given to test the reader's grasp of the ideas.
Review
"[An] excellent book on field theory written from a modern standpoint and using a mathematical language (that of 'functional methods') appropriate to this standpoint. A superior text. Bellac's book surveys the whole field, but is particularly good on the physics of condensed matter. It is written in a very clear way. He covers a lot of ground, but in such a way that a beginning research student can learn about topics as diverse as the ising model, the renormalization group, path integral methods, and non-abelian gauge field theories. In fact, the earlier sections of the book should accessible to final-year undergraduates in theoretical physics. The book is well planned, carefully written, and pedagogically sound." --???
"Good undergraduates, graduate students, teachers at different levels, and curious scientists are among the potential readers of this very interesting book."--Journal of Statistical Physics
Description
Includes bibliographical references (p. [585]-588) and index.
Table of Contents
PART I: Critical Phenomena 1. Introduction to Critical Phenomena
2. Landau Theory
3. The Renormalization Group
4. Two-Dimensional Models
PART II: Perturbation Theory and Renormalization--The Euclidean Scalar Field
5. The Perturbation Expansion and Feynman Diagrams
6. Renormalization
7. The Callan-Symanzik Equations
PART III: The Quantum Theory of Scalar Fields
8. Path Integrals in Quantum and in Statistical Mechanics
9. Quantization of the Klein-Gordon Field
10. Green's Functions and the S Matrix
PART IV: Gauge Theories
11. Quantization of the Dirac Field and the Electromagnetic Field
12. Quantum Electrodynamics
13. Non-Abelian Gauge Theories