Functional integration : action and symmetries
著者
書誌事項
Functional integration : action and symmetries
(Cambridge monographs on mathematical physics)
Cambridge University Press, c2006
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内容説明・目次
内容説明
Functional integration successfully entered physics as path integrals in the 1942 PhD dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.
目次
- 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.
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