This course in modern quantum field theory for condensed matter physics includes a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals. Alexei Tsvelik also covers Landau Fermi liquid theory and 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. First edition Hb (1995): 0-521-45467-0 First edition Pb (1996): 0-521-58989-4
|Publisher:||Cambridge University Press|
|Product dimensions:||6.85(w) x 9.72(h) x 0.79(d)|
Table of ContentsPreface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 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 transformations 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; Part IV. Physics in the World of One Spatial Dimension: Introduction; 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; Select bibliography; Index.