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E-grāmata: Functional Integration: Action and Symmetries

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(University of Texas, Austin), (Institut des Hautes Études Scientifiques, France)
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Functional Integration: Action and SymmetriesPalielināt
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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.

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

Recenzijas

Review of the hardback: 'will be helpful for those mathematicians who are interested in physical applications of the general theory of measure (theory of integrals) and for the physicists who are interested in mathematically rigorous formulations of complicated problems in quantum physics.' Zentralblatt MATH 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

Papildus informācija

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


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.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97805112583292e.html
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