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Functional Integration: Action and Symmetries

Pierre Cartier and Cécile DeWitt-Morette
Publisher: 
Cambridge University Press
Publication Date: 
2007
Number of Pages: 
456
Format: 
Hardcover
Series: 
Cambridge Monographs on Mathematical Physics
Price: 
140.00
ISBN: 
9780521866965
Category: 
Monograph
We do not plan to review this book.

 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.

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