Functional Integration

Erscheinungsjahr 2016
ISBN: 978-0-521-86696-5
Verlag: Cambridge University Press

Buch, Englisch, 476 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 997 g

Reihe: Cambridge Monographs on Mathematical Physics

Functional integration successfully entered physics as path integrals in the 1942 Ph.D. 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 new 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; Aharanov-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.

Autoren/Hrsg.

Cartier, Pierre

DeWitt-Morette, Cecile

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Angewandte Physik Soziophysik, Wirtschaftsphysik

Inhaltsverzeichnis

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 Marcus Bery; 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. Jacobi operator; Appendix F. Change of variables of integration; Bibliography; Index.

Über Autor(innen)

DeWitt-Morette, Cecile
Jane and Roland Blumberg Centennial Professor in Physics, Emerita, University of Texas at Austin. Member of American and European Physical Societies.

Cartier, Pierre
Emeritus Director of Research, Center National de la Recherche Scientifique, France. Member of Societe Francaise de Mathematiques and American Mathematical Society.