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About This Book
Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group isdeveloped and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with BohmâPines and ChernâSimons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.
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Table of contents
- Cover
- Half-title
- Title page
- Copyright information
- Dedication
- Table of contents
- Preface
- 1 Thermodynamics and Statistical Mechanics Review
- 2 The Ising Model in d=0 and d=1
- 3 Statistical to Quantum Mechanics
- 4 Quantum to Statistical Mechanics
- 5 The Feynman Path Integral
- 6 Coherent State Path Integrals for Spins, Bosons, and Fermions
- 7 The Two-Dimensional Ising Model
- 8 Exact Solution of the Two-Dimensional Ising Model
- 9 Majorana Fermions
- 10 Gauge Theories
- 11 The Renormalization Group
- 12 Critical Phenomena: The Puzzle and Resolution
- 13 Renormalization Group for the Ď<sup>4<sup> Model
- 14 Two Views of Renormalization
- 15 Renormalization Group for Non-Relativistic Fermions: I
- 16 Renormalization Group for Non-Relativistic Fermions: II
- 17 Bosonization I: The FermionâBoson Dictionary
- 18 Bosonization II: Selected Applications
- 19 Duality and Triality
- 20 Techniques for the Quantum Hall Effect
- Index