Methods of Contemporary Gauge Theory

Introduces the quantum theory of gauge fields through four non-perturbative methods with important applications; reissued as Open Access.

Yuri Makeenko (Author)

9781009402101, Cambridge University Press

Paperback / softback, published 27 July 2023

430 pages
24.5 x 16.9 x 2.5 cm, 0.75 kg

This book introduces the quantum theory of gauge fields, emphasising four non-perturbative methods which have important applications: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are 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 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. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.

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: Statistical physics [PHS]