Functional integration : action and symmetries
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Bibliographic Information
Functional integration : action and symmetries
（Cambridge monographs on mathematical physics）
Cambridge University Press, c2006
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Description and Table of Contents
Description
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.
Table of Contents
- 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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