Functional Integration: Action and Symmetries

ISBN: 9780521143578 出版年：2006 页码：478 Pierre Cartier Cecile DeWitt-Morette Cambridge University Press

Acknowledgements List symbols, conventions, and formulary Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment Part II. Quantum Mechanics: 2. First lesson: gaussian integrals 3. Selected examples 4. Semiclassical expansion: WKB 5. Semiclassical expansion: beyond WKB 6. Quantum dynamics: path integrals and operator formalism Part III. Methods from Differential Geometry: 7. Symmetries 8. Homotopy 9. Grassmann analysis: basics 10. Grassmann analysis: applications 11. Volume elements, divergences, gradients Part IV. Non-Gaussian Applications: 12. Poisson processes in physics 13. A mathematical theory of Poisson processes 14. First exit time: energy problems Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction 16. Renormalization 2: scaling 17. Renormalization 3: combinatorics 18. Volume elements in quantum field theory Bryce DeWitt Part VI. Projects: 19. Projects Appendix A. Forward and backward integrals: spaces of pointed paths Appendix B. Product integrals Appendix C. A compendium of gaussian integrals Appendix D. Wick calculus Alexander Wurm Appendix E. The Jacobi operator Appendix F. Change of variables of integration Appendix G. Analytic properties of covariances Appendix H. Feynman's checkerboard Bibliography Index.