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Informationen zum Autor Emeritus Director of Research! Center National de la Recherche Scientifique! France. Member of Societe Francaise de Mathematiques and American Mathematical Society. Jane and Roland Blumberg Centennial Professor in Physics! Emerita! University of Texas at Austin. Member of American and European Physical Societies. Klappentext The powerful tool of functional integration is widely applied and shown to be user-friendly and mathematically robust. Zusammenfassung In this text! Cartier and DeWitt-Morette! using their complementary interests and expertise! successfully condense and apply the essentials of Functional Integration to a great variety of systems! showing this mathematically elusive technique to be a robust! user friendly and multipurpose tool. 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....
