内容

目次

Introduction to path integrals: Quantum mechanics. Fermions. Functional integrals in field theory. Further comments on functional methods. Green functions in field theory. Application of the saddle point method to functional integrals. Some simple calculations: Harmonic oscillator in quantum mechanics. Ground state energy. Double well potential and instantons. Role of instantons. Supersymmetric quantum mechanics. Grassmannian models and their classical solutions: Introduction - a few comments about Yang Mills theories. Grassmannian sigma-models and their instanton solutions. Properties of the solutions of the G(M,N) models. Quantum Fluctuations: The case of instantons. Noninstanton case. Sigma models with fermions: CPN-1 model with fermions. Dirac background problem. Full supersymmetric model. 1/N limits: 1/N expansion in quantum mechanics. 1/N expansion in theory. 1/N expansion of the CPN-1 model. Chiral models: Introduction. Uhlenbeck's equations and their simple solutions. Solutions of the U(4) model. General one-uniton solutions. Properties of our solutions. Sigma models with the Wess-Zumino term: Lax-pair problem. The Wess-Zumino term. U(N) model with the Wess-Zumino term. Solutions of the WZ-sigma model. Properties of the solutions. More general models: Introduction. Supersymmetric extensions. Anomaly in two-dimensions. Skyrme models: The Skyrme idea. CP1 Skyrmions. CPN-1 Skyrmions. Non-instanton solutions. The Hopf term. Appendices. References