Pierre Cartier: Functional Integration

Cover: 9780521143578 | Functional Integration | Action and Symmetries | Cartier (u. a.)

Rückseite: 9780521143578 | Functional Integration | Action and Symmetries | Cartier (u. a.)

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Sprache: Englisch

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Beschreibung

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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2010
Genre:	Importe , Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9780521143578
ISBN-10:	0521143578
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Cartier, Pierre Dewitt-Morette, Cecile
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	244 x 170 x 26 mm
Von/Mit:	Pierre Cartier (u. a.)
Erscheinungsdatum:	02.06.2010
Gewicht:	0,821 kg