内容

目次

Part I. Introduction to Methods: 1. QFT - language and goals; 2. Pathintegral; 3. Definitions of correlation functions. Wick's theorem; 4.Free bosonic field in external field; 5. Perturbation theory. Feynmandiagrams; 6. Methods of calculation of diagram series; 7.Renormalization group procedures; 8. O(N)-symmetric vector model belowthe transition point; 9. Non-linear sigma models in two dimensions; 10.O(3)-nonlinear sigma model in the strong coupling limit; Part II.Fermions: 11. Path integrals and Wick's theorem for fermions; 12.Electrodynamics in metals; 13. Relativistic fermions; 14. Aharonov-Bohmeffect and transmutation of statistics in (2 + 1) dimensions; Part III.Strongly Fluctuating Spin Systems: 15. Schwinger-Wigner quantizationprocedure; 16. O(3)-nonlinear sigma model in (2 + 1) dimensions; 17.Order from disorder; 18. Jordan Wigner transformation for spin S = 1/2models in D = 1, 2, 3; 19. Majorana representation for spin S = 1/2magnets; 20. Path integral representations; Part IV. Physics in theWorld of One Spatial Dimension: 21. The model of free bosonic masslessscalar field; 22. Relevant and irrelevant fields; 23.Kosterlitz-Thouless transition; 24. Conformal symmetry; 25. Definitionof conformal invariance; 26. Ising model; 27. Spin S = 1/2 Heisenbergchain; 28. One dimensional fermions with spin; 29. Non-Abelianbosonization, Katz-Moody algebras, Wess-Zumino-Witten model; 30.Wess-Zumino-Witten model in the Lagrangian form; 31. (1 + 1)dimensional quantum chromodynamics; 32. Spin S = 1 Heisenberg chain;33. Kondo chain; 34. Conformal theory cookbook; 35. Conclusion.