Non-Perturbative Quantum Field Theory : An Introduction to Topological and Semiclassical Methods

Abstract

This book presents in a systematic fashion a number of quantum field theoretic phenomena that have a topological underpinning. The systematics is provided by the homotopy groups of the configuration space: solitons and instantons are related to the zeroth and first homotopy groups respectively, and quantized parameters to the second. The close relation of some of these notions to anomalies is also discussed. These concepts have many applications, from particle physics to statistical and condensed matter physics. The focus is mainly on the former, but some particularly instructive examples of the latter are also described.