Functional Integration
Action and Symmetries

The powerful tool of functional integration is widely applied and shown to be user-friendly and mathematically robust.

Pierre Cartier (Author), Cecile DeWitt-Morette (Author)

9780521143578, Cambridge University Press

Paperback, published 10 June 2010

480 pages
24.4 x 17 x 2.5 cm, 0.76 kg

Review of the hardback: '…for someone who is interested in the mathematical foundations or merely curious to see some of the deep insight of two true experts, Cartier and DeWitt-Morette's book is well worth reading.' Physics Today

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.

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.

Subject Areas: Statistical physics [PHS]