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Condensed Matter Field Theory, Second Edition

Book Description

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.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. 1 From particles to fields
    1. 1.1 Classical harmonic chain: phonons
    2. 1.2 Functional analysis and variational principles
    3. 1.3 Maxwell’s equations as a variational principle
    4. 1.4 Quantum chain
    5. 1.5 Quantum electrodynamics
    6. 1.6 Noether’s theorem
    7. 1.7 Summary and outlook
    8. 1.8 Problems
  7. 2 Second quantization
    1. 2.1 Introduction to second quantization
    2. 2.2 Applications of second quantization
    3. 2.3 Summary and outlook
    4. 2.4 Problems
  8. 3 Feynman path integral
    1. 3.1 The path integral: general formalism
    2. 3.2 Construction of the path integral
    3. 3.3 Applications of the Feynman path integral
    4. 3.4 Summary and outlook
    5. 3.5 Problems
  9. 4 Functional field integral
    1. 4.1 Construction of the many-body path integral
    2. 4.2 Field integral for the quantum partition function
    3. 4.3 Field theoretical bosonization: a case study
    4. 4.4 Summary and outlook
    5. 4.5 Problems
  10. 5 Perturbation theory
    1. 5.1 General structures and low-order expansions
    2. 5.2 Ground state energy of the interacting electron gas
    3. 5.3 Infinite-order expansions
    4. 5.4 Summary and outlook
    5. 5.5 Problems
  11. 6 Broken symmetry and collective phenomena
    1. 6.1 Mean-field theory
    2. 6.2 Plasma theory of the interacting electron gas
    3. 6.3 Bose–Einstein condensation and superfluidity
    4. 6.4 Superconductivity
    5. 6.5 Field theory of the disordered electron gas
    6. 6.6 Summary and outlook
    7. 6.7 Problems
  12. 7 Response functions
    1. 7.1 Crash course in modern experimental techniques
    2. 7.2 Linear response theory
    3. 7.3 Analytic structure of correlation functions
    4. 7.4 Electromagnetic linear response
    5. 7.5 Summary and outlook
    6. 7.6 Problems
  13. 8 The renormalization group
    1. 8.1 The one-dimensional Ising model
    2. 8.2 Dissipative quantum tunneling
    3. 8.3 Renormalization group: general theory
    4. 8.4 RG analysis of the ferromagnetic transition
    5. 8.5 RG analysis of the nonlinear σ-model
    6. 8.6 Berezinskii–Kosterlitz–Thouless transition
    7. 8.7 Summary and outlook
    8. 8.8 Problems
  14. 9 Topology
    1. 9.1 Example: particle on a ring
    2. 9.2 Homotopy
    3. 9.3 θ-terms
    4. 9.4 Wess–Zumino terms
    5. 9.5 Chern–Simons terms
    6. 9.6 Summary and outlook
    7. 9.7 Problems
  15. 10 Nonequilibrium (classical)
    1. 10.1 Fundamental questions of (nonequilibrium) statistical mechanics
    2. 10.2 Langevin theory
    3. 10.3 Boltzmann kinetic theory
    4. 10.4 Stochastic processes
    5. 10.5 Field theory I: zero dimensional theories
    6. 10.6 Field theory II: higher dimensions
    7. 10.7 Field theory III: applications
    8. 10.8 Summary and Outlook
    9. 10.9 Problems
  16. 11 Nonequilibrium (quantum)
    1. 11.1 Prelude: Quantum master equation
    2. 11.2 Keldysh formalism: basics
    3. 11.3 Particle coupled to an environment
    4. 11.4 Fermion Keldysh theory (a list of changes)
    5. 11.5 Kinetic equation
    6. 11.6 A mesoscopic application
    7. 11.7 Full counting statistics
    8. 11.8 Summary and outlook
    9. 11.9 Problems
  17. Index