Makeenko, Y.

2023
Cambridge University Press Cambridge

Abstract: 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.

Keyword(s): thema EDItEUR::P Mathematics and Science::PH Physics::PHN Nuclear physics ; path Integrals ; operator calculus ; second quantization ; quantum anomalies ; instantons ; lattice gauge theories ; gauge fields on a lattice ; lattice methods ; fermions on a lattice ; finite temperatures ; 1/N expansion ; O(N) vector models ; multicolor QCD ; QCD in loop space ; matrix models ; reduced models ; Eguchi–Kawai model ; twisted reduced models ; non-commutative gauge theories ; Textbook ; Particle Physics and Nuclear Physics ; Physics and Astronomy ; Theoretical Physics and Mathematical Physics