Methods of Contemporary Gauge Theory

This 2002 book is a thorough introduction to quantum theory of gauge fields, with emphasis on modern non-perturbative methods.

Yuri Makeenko (Author)

9780521022156, Cambridge University Press

Paperback, published 3 November 2005

432 pages, 133 exercises
24.5 x 17.2 x 2.5 cm, 0.681 kg

' … the book is a valuable source of information on recent developments for advanced students.' Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

Preface
Part I. Path Integrals: 1. Operator calculus
2. Second quantization
3. Quantum anomalies from path integral
4. Instantons in quantum mechanics
Part II. Lattice Gauge Theories: 5. Observables in gauge theories
6. Gauge fields on a lattice
7. Lattice methods
8. Fermions on a lattice
9. Finite temperatures
Part III. 1/N Expansion: 10. O(N) vector models
11. Multicolor QCD
12. QCD in loop space
13. Matrix models
Part IV. Reduced Models: 14. Eguchi–Kawai model
15. Twisted reduced models
16. Non-commutative gauge theories.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Particle & high-energy physics [PHP], Condensed matter physics [liquid state & solid state physics PHFC]