Quantum field theory in condensed matter physics 2nd Edition by Alexei Tsvelik 0521529808 9780521529808
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ISBN 10: 0521529808
ISBN 13: 9780521529808
Author: Alexei Tsvelik
This book is a course in modern quantum field theory as seen through the eyes of a theorist working in condensed matter physics. It contains a gentle introduction to the subject and therefore can be used even by graduate students. The introductory parts include a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals including a discussion of Landau–Fermi liquid theory. In later chapters the discussion gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.
Quantum field theory in condensed matter physics 2nd Table of contents:
I: Introduction to Methods
- QFT: language and goals
- Connection between quantum and classical: path integrals
- Definitions of correlation functions: Wick’s theorem
- Free bosonic field in an external field
- Perturbation theory: Feynman diagrams
- Calculation methods for diagram series: divergences and their elimination
- Renormalization group procedures
- O(N)-symmetric vector model below the transition point
- Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion
- O(3) nonlinear sigma model in the strong coupling limit
II: Fermions
11. Path integral and Wick’s theorem for fermions
12. Interacting electrons: the Fermi liquid
13. Electrodynamics in metals
14. Relativistic fermions: aspects of quantum electrodynamics
15. Aharonov–Bohm effect and transmutation of statistics
III: Strongly Fluctuating Spin Systems
16. Schwinger–Wigner quantization procedure: nonlinear sigma models
17. O(3) nonlinear sigma model in (2 + 1) dimensions: the phase diagram
18. Order from disorder
19. Jordan–Wigner transformation for spin S = 1/2 models in D = 1, 2, 3
20. Majorana representation for spin S = 1/2 magnets: relationship to Z₂ lattice gauge theories
21. Path integral representations for a doped antiferromagnet
IV: Physics in the World of One Spatial Dimension
22. Model of the free bosonic massless scalar field
23. Relevant and irrelevant fields
24. Kosterlitz–Thouless transition
25. Conformal symmetry
26. Virasoro algebra
27. Differential equations for the correlation functions
28. Ising model
29. One-dimensional spinless fermions: Tomonaga–Luttinger liquid
30. One-dimensional fermions with spin: spin-charge separation
31. Kac–Moody algebras: Wess–Zumino–Novikov–Witten model
32. Wess–Zumino–Novikov–Witten model in the Lagrangian form: non-Abelian bosonization
33. Semiclassical approach to Wess–Zumino–Novikov–Witten models
34. Integrable models: dynamical mass generation
35. A comparative study of dynamical mass generation in one and three dimensions
36. One-dimensional spin liquids: spin ladder and spin S = 1 Heisenberg chain
37. Kondo chain
38. Gauge fixing in non-Abelian theories: (1 + 1)-dimensional quantum chromodynamics
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