Functional integration : action and symmetries

著者

• Cartier, Pierre
• DeWitt-Morette, Cécile

書誌事項

Functional integration : action and symmetries

P. Cartier and C. Dewitt-Morette

（Cambridge monographs on mathematical physics）

Cambridge University Press, 2010, c2006

• : pbk

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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詳細情報

• NII書誌ID(NCID): BB04101907
• ISBN:
  • 9780521143578
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge, UK
• ページ数/冊数: xx, 456 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA00074521