内容

目次

Part I. Introduction to Methods: 1. QFT: language and goals; 2.Connection between quantum and classical: path integrals; 3. Definitions ofcorrelation functions: Wick's theorem; 4. Free bosonic field in an externalfield; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods fordiagram series: divergences and their elimination; 7. Renormalization groupprocedures; 8. O(N)-symmetric vector model below the transition point; 9.Nonlinear sigma models in two dimensions: renormalization group and1/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 concept of a Fermi liquid; 13. Electrodynamics inmetals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15.Aharonov-Bohm effect and transmutation of statistics; Part III. StronglyFluctuating 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 transformationsfor spin S=1/2 models in D=1, 2, 3; 20. Majorana representations for spinS=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integralrepresentations for a doped antiferromagnet; Part IV. Physics in the World ofOne 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 thecorrelation functions; 28. Ising model; 29. One-dimensional spinlessfermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin:spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Wittenmodel; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form:non-Abelian bosonization; 33. Semiclassical approach to WZNW models; 34.Integrable models: dynamical mass generation; 35. A comparative study ofdynamical mass generation in one and three dimensions; 36. One-dimensionalspin liquids: spin ladder and spin S=1 Heisenberg chain; 37. Kondo chain; 38.Gauge fixing in non-Abelian theories: (1+1)-dimensional quantumchromodynamics.