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Theoretical condensed matter physics draws heavily and increasingly on the language of quantum field theory. This primer is aimed at elevating graduate students of condensed matter physics to a level where they can engage in independent research. It emphasizes the development of modem methods of classical and quantum field theory with applicati*** of interest in both experimental and theoretical condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual ***ects and formal methodology are emphasized and developed, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked soluti***, designed to provide a bridge between formal manipulati*** and research-oriented thinking.

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 Feymnan 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 Summary and outlook

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

7 Resp***e functi***

7.1 Crash course in modem 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: generaltheory

8.4 RG ***ysis of the ferromagnetic transition

8.5 RG ***ysis of the nonlinear o'-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 0-Terms

9.4 Wess-Zumino terms

9.5 Chern-Sim*** terms

9.6 Summary and outlook

9.7 Problems

Index

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本书由世界图书出版公司北京公司和剑桥大学出版社合作出版。

书籍介绍

Theoretical condensed matter physics draws heavily and increasingly on the language of quantum field theory. This primer is aimed at elevating graduate students of condensed matter physics to a level where they can engage in independent research. It emphasizes the development of modem methods of classical and quantum field theory with applicati*** of interest in both experimental and theoretical condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual ***ects and formal methodology are emphasized and developed, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked soluti***, designed to provide a bridge between formal manipulati*** and research-oriented thinking.