The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.

Table of Contents

Part I

1 From Particles to Fields

2 Second Quantization

3 Path Integral

4 Perturbation Theory

5 Broken Symmetry and Collective Phenomena

6 Renormalization Group

7 Response Functions

Part II

8 Topological Field Theory

9 Relativistic Field Theory

10 Gauge Theory

11 Nonequilibrium (Classical)

12 Nonequilibrium (Quantum)

About the Authors

Alexander Altland is Professor of Theoretical Physics at the University of Cologne. He is a field theorist who has worked in various areas of condensed matter physics and neighbouring fields. His research interests include the physics of disordered and chaotic systems, and connections between condensed matter and particle physics.

Ben Simons is the Royal Society EP Abraham Professor and Herchel Smith Professor of Physics at the University of Cambridge. His research has spanned a broad range of areas in condensed matter and statistical physics, from disordered normal and superconducting compounds to correlated electron and light-matter systems, and biological physics.