Condensed Matter Field Theory

by Alexander Altland , Ben D. Simons

• ISBN13: 9780521769754
• ISBN10: 0521769752
• Edition: 2nd
• Format: Hardcover
• Copyright: 2010-04-30
• Publisher: Cambridge University Press

Summary

Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum 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 renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations 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.

Author Biography

Alexander Altland is Professor of Theoretical Condensed Matter Physics at the Institute of Theoretical Physics, University of Koln. His main areas of research include mesoscopic physics, the physics of interacting many particle systems, and quantum nonlinear dynamics
Ben Simons is Professor of Theoretical Condensed Matter Physics at the Cavendish Laboratory, University of cambridege. His main areas of research include strongly correlated condensed matters systems, mesoscopic and ultracold atom physics.

Table of Contents

Preface	p. ix
From particles to fields	p. 1
Classical harmonic chain: phonons	p. 3
Functional analysis and variational principles	p. 11
Maxwell's equations as a variational principle	p. 15
Quantum chain	p. 19
Quantum electrodynamics	p. 24
Noether's theorem	p. 30
Summary and outlook	p. 34
Problems	p. 35
Second quantization	p. 39
Introduction to second quantization	p. 40
Applications of second quantization	p. 50
Summary and outlook	p. 83
Problems	p. 83
Feynman path integral	p. 95
The path integral: general formalism	p. 95
Construction of the path integral	p. 97
Applications of the Feynman path integral	p. 112
Problems	p. 146
Problems	p. 146
Functional field integral	p. 156
Construction of the many-body path integral	p. 158
Field integral for the quantum partition function	p. 165
Field theoretical bosonization: a case study	p. 173
Summary and outlook	p. 181
Problems	p. 181
Perturbation theory	p. 193
General structures and low-order expansions	p. 194
Ground state energy of the interacting electron gas	p. 208
Infinite-order expansions	p. 223
Summary and outlook	p. 232
Problems	p. 233
Broken symmetry and collective phenomena	p. 242
Mean-field theory	p. 243
Plasma theory of the interacting electron gas	p. 243
Bose-Einstein condensation and superfluidity	p. 251
Superconductivity	p. 265
Field theory of the disordered electron gas	p. 301
Summary and outlook	p. 329
Problems	p. 331
Response functions	p. 360
Crash course in modern experimental techniques	p. 360
Linear response theory	p. 368
Analytic structure of correlation functions	p. 372
Electromagnetic linear response	p. 389
Summary and outlook	p. 399
Problems	p. 400
The renormalization group	p. 409
The one-dimensional Ising model	p. 412
Dissipative quantum tunneling	p. 422
Renormalization group: general theory	p. 429
RG analysis of the ferromagnetic transition	p. 444
RG analysis of the nonlinear ¿-model	p. 456
Berezinskii-Kosterlitz-Thouless transition	p. 463
Summary and outlook	p. 474
Problems	p. 475
Topology	p. 496
Example: particle on a ring	p. 497
Homotopy	p. 502
¿-Oterms	p. 505
Wess-Zumino terms	p. 536
Chern-Simons terms	p. 569
Summary and outlook	p. 588
Problems	p. 588
Nonequilibrium (classical)	p. 602
Fundamental questions of (nonequilibrium) statistical mechanics	p. 607
Langevin theory	p. 609
Boltzmann kinetic theory	p. 623
Stochastic processes	p. 632
Field theory I: zero dimensional theories	p. 643
Field theory II: higher dimensions	p. 654
Field theory III: applications	p. 665
Summary and Outlook	p. 684
Problems	p. 684
Nonequilibrium (quantum)	p. 693
Prelude: Quantum master equation	p. 695
Keldysh formalism: basics	p. 700
Particle coupled to an environment	p. 716
Fermion Keldysh theory (a list of changes)	p. 720
Kinetic equation	p. 723
A mesoscopic application	p. 729
Full counting statistics	p. 745
Summary and outlook	p. 753
Problems	p. 753
Index	p. 766
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