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Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quan-tum field theory in many particle physics, emphasizing the applicability of the formalism to concrete problems.

This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormaliza-tion group methods, the theory of resp***e functi***, and topology. Conceptual ***ects and formal methodology are emphasized, but the discussion focuses on practical experimental applicati*** drawn largely from condensed matter physics and neighboring fields.

Extended and challenging problems with fully–worked soluti*** provide a bridge between formal manipulati*** and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many particle theory.

Preface

1 From particles to fields

1.1 Classical harmonic chain： phon***

1.2 Functional ***ysis and variational principles

1.3 Maxwell’s equati*** as a variational principle

1.4 Quantum chain

1.5 Quantum electrodynamics

1.6 Noether’s theorem

1.7 Summary and outlook

1.8 Problems

2 Second quantization

2.1 Introduction to second quantization

2.2 Applicati*** of second quantization

2.3 Summary and outlook

2.4 Problems

3 Feynman path integral

3.1 The path integral： general formalism

3.2 C***truction of the path integral

3.3 Applicati*** of the Feynman path integral

3.4 Problems

3.5 Problems

4 Functional field integral

4.1 C***truction of the many—body path integral

4.2 Field integral for the quantum partition function

4.3 Field theoretical bosonization： a case study

4.4 Summary and outlook

4.5 Problems

5 Perturbation theory

5.1 General structures and low—order expansi***

5.2 Ground state energy of the in***cting electron gas

5.3 Infinite—order expansi***

5.4 Summary and outlook

5.5 Problems

6 Broken symmetry and collective phenomena

6.1 Mean—field theory

6.2 Plasma theory of the in***cting electron gas

6.3 Bose—Einstein condensation and superfluidity

*** Superconductivity

6.5 Field theory of the disordered electron gas

6.6 Summary and outlook

6.7 Problems

Resp***e functi***

7.1 Crash course in modern experimental techniques

7.2 Linear resp***e theory

7.3 Analytic structure of correlation functi***

7.4 Electromagnetic linear resp***e

7.5 Summary and outlook

7.6 Problems

8 The renormalization group

8.1 The one—dimensional Ising model

8.2 Dissipative quantum tunneling

8.3 Renormalization group： general theory

8.4 RG ***ysis of the ferromagnetic transition

8.5 RG ***ysis of the nonlinear σ—model

8.6 Berezinskii—Kosterlitz—Thouless transition

8.7 Summary and outlook

8.8 Problems

9 Topology

9.1 Example： particle on a ring

9.2 Homotopy

9.3 θ—Oterms

9.4 Wess—Zurnino terms

9.5 Chern—Sim*** terms

9.6 Summary and outlook

9.7 Problems

10 Nonequilibrium （classical）

10.1 Fundamental questi*** of （nonequilibrium） statistical mechanics

10.2 Langevin theory

10.3 Boltzmann kinetic theory

10.4 Stochastic processes

10.5 Field theory Ⅰ： zero dimensional theories

10.6 Field theory Ⅱ： higher dimensi***

10.7 Field theory Ⅲ： applicati***

10.8 Summary and Outlook

10.9 Problems

11 Nonequilibrium （quantum）

11.1 Prelude： Quantum master equation

11.2 Keldysh formalism： basics

11.3 Particle coupled to an environment

11.4 Fermion Keldysh theory （a list of changes）

11.5 Kinetic equation

11.6 A mesoscopic application

11.7 Full counting statistics

11.8 Summary and outlook

11.9 Problems

Index

Alexander Altland is Professor of Theoretical Condensed Matter Physics at the Institute of Theoretical Physics, University of K¨oln. His main areas of research include mesoscopic physics, the physics of in***cting many particle systems, and quantum nonlinear dynamics.

Benjamin D. Sim*** is Professor of Theoretical Condensed Matter Physics at the

Cavendish Laboratory, University of Cambridge. His main areas of research include strongly correlated condensed matter systems, mesoscopic and ultracold atom physics.

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书籍介绍

Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quan-tum field theory in many particle physics, emphasizing the applicability of the formalism to concrete problems.

This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormaliza-tion group methods, the theory of resp***e functi***, and topology. Conceptual ***ects and formal methodology are emphasized, but the discussion focuses on practical experimental applicati*** drawn largely from condensed matter physics and neighboring fields.

Extended and challenging problems with fully–worked soluti*** provide a bridge between formal manipulati*** and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many particle theory.