Functional integration: action and symmetries
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 fresh approach to functional integration. The book is self-co...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-92 Volltext |
| Zusammenfassung: | 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 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 456 pages) |
| ISBN: | 9780511535062 |
| DOI: | 10.1017/CBO9780511535062 |
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| 505 | 8 | |a The physical and mathematical environment -- An inheritance from physics -- A toolkit from analysis -- Feynman's integral versus Kac's integral -- Quantum mechanics -- First lesson : gaussian integrals -- Semiclassical expansion : WKB -- Semiclassical expension : beyond WKB -- Quantum dynamics : path integrals and the operator formalism -- Methods from differential geometry -- Symmetries -- Homotopy -- Grassmann analysis : basics -- Grassmann analysis : applications -- Volume elements, divergences, gradients -- Non-gaussian applications -- Poisson processes in physics -- A mathematical theory of Poisson processes -- The first exit time : energy problems -- Problems in quantum field theory -- Renormalization 1 : an introduction -- Renormalization 2 : scaling -- Renormalization 3 : combinatorics / contributed by Markus Berg -- Volume elements in quantum field theory / contributed by Bryce DeWitt -- Projects -- Appendix A : Forward and backward integrals, spaces of pointed paths -- Appendix B : Product integrals -- Appendix C : A compedium of gaussian integrals -- Appendix D : Wick calculus / contributed by 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 | |
| 520 | |a 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 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 | ||
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Datensatz im Suchindex
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| author | Cartier, Pierre 1932-2024 |
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| author_role | aut |
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| author_variant | p c pc |
| building | Verbundindex |
| bvnumber | BV043942033 |
| classification_rvk | UK 1200 UK 4500 |
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| contents | The physical and mathematical environment -- An inheritance from physics -- A toolkit from analysis -- Feynman's integral versus Kac's integral -- Quantum mechanics -- First lesson : gaussian integrals -- Semiclassical expansion : WKB -- Semiclassical expension : beyond WKB -- Quantum dynamics : path integrals and the operator formalism -- Methods from differential geometry -- Symmetries -- Homotopy -- Grassmann analysis : basics -- Grassmann analysis : applications -- Volume elements, divergences, gradients -- Non-gaussian applications -- Poisson processes in physics -- A mathematical theory of Poisson processes -- The first exit time : energy problems -- Problems in quantum field theory -- Renormalization 1 : an introduction -- Renormalization 2 : scaling -- Renormalization 3 : combinatorics / contributed by Markus Berg -- Volume elements in quantum field theory / contributed by Bryce DeWitt -- Projects -- Appendix A : Forward and backward integrals, spaces of pointed paths -- Appendix B : Product integrals -- Appendix C : A compedium of gaussian integrals -- Appendix D : Wick calculus / contributed by 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511535062 (OCoLC)992870068 (DE-599)BVBBV043942033 |
| dewey-full | 530.1557 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1557 |
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| discipline | Physik |
| doi_str_mv | 10.1017/CBO9780511535062 |
| format | Electronic eBook |
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| id | DE-604.BV043942033 |
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| indexdate | 2024-08-21T00:08:06Z |
| institution | BVB |
| isbn | 9780511535062 |
| language | English |
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| publishDate | 2006 |
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| publisher | Cambridge University Press |
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| spelling | Cartier, Pierre 1932-2024 Verfasser (DE-588)141948256 aut Functional integration action and symmetries Pierre Cartier and Cécile DeWitt-Morette Cambridge Cambridge University Press 2006 1 online resource (xx, 456 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge monographs on mathematical physics Title from publisher's bibliographic system (viewed on 05 Oct 2015) The physical and mathematical environment -- An inheritance from physics -- A toolkit from analysis -- Feynman's integral versus Kac's integral -- Quantum mechanics -- First lesson : gaussian integrals -- Semiclassical expansion : WKB -- Semiclassical expension : beyond WKB -- Quantum dynamics : path integrals and the operator formalism -- Methods from differential geometry -- Symmetries -- Homotopy -- Grassmann analysis : basics -- Grassmann analysis : applications -- Volume elements, divergences, gradients -- Non-gaussian applications -- Poisson processes in physics -- A mathematical theory of Poisson processes -- The first exit time : energy problems -- Problems in quantum field theory -- Renormalization 1 : an introduction -- Renormalization 2 : scaling -- Renormalization 3 : combinatorics / contributed by Markus Berg -- Volume elements in quantum field theory / contributed by Bryce DeWitt -- Projects -- Appendix A : Forward and backward integrals, spaces of pointed paths -- Appendix B : Product integrals -- Appendix C : A compedium of gaussian integrals -- Appendix D : Wick calculus / contributed by 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 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 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 Integration, Functional Funktionalintegration (DE-588)4155674-4 gnd rswk-swf Funktionalintegration (DE-588)4155674-4 s 1\p DE-604 DeWitt-Morette, Cécile 1922-2017 Sonstige (DE-588)141948361 oth Erscheint auch als Druckausgabe 978-0-521-14357-8 Erscheint auch als Druckausgabe 978-0-521-86696-5 https://doi.org/10.1017/CBO9780511535062 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cartier, Pierre 1932-2024 Functional integration action and symmetries The physical and mathematical environment -- An inheritance from physics -- A toolkit from analysis -- Feynman's integral versus Kac's integral -- Quantum mechanics -- First lesson : gaussian integrals -- Semiclassical expansion : WKB -- Semiclassical expension : beyond WKB -- Quantum dynamics : path integrals and the operator formalism -- Methods from differential geometry -- Symmetries -- Homotopy -- Grassmann analysis : basics -- Grassmann analysis : applications -- Volume elements, divergences, gradients -- Non-gaussian applications -- Poisson processes in physics -- A mathematical theory of Poisson processes -- The first exit time : energy problems -- Problems in quantum field theory -- Renormalization 1 : an introduction -- Renormalization 2 : scaling -- Renormalization 3 : combinatorics / contributed by Markus Berg -- Volume elements in quantum field theory / contributed by Bryce DeWitt -- Projects -- Appendix A : Forward and backward integrals, spaces of pointed paths -- Appendix B : Product integrals -- Appendix C : A compedium of gaussian integrals -- Appendix D : Wick calculus / contributed by 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 Integration, Functional Funktionalintegration (DE-588)4155674-4 gnd |
| subject_GND | (DE-588)4155674-4 |
| title | Functional integration action and symmetries |
| title_auth | Functional integration action and symmetries |
| title_exact_search | Functional integration action and symmetries |
| title_full | Functional integration action and symmetries Pierre Cartier and Cécile DeWitt-Morette |
| title_fullStr | Functional integration action and symmetries Pierre Cartier and Cécile DeWitt-Morette |
| title_full_unstemmed | Functional integration action and symmetries Pierre Cartier and Cécile DeWitt-Morette |
| title_short | Functional integration |
| title_sort | functional integration action and symmetries |
| title_sub | action and symmetries |
| topic | Integration, Functional Funktionalintegration (DE-588)4155674-4 gnd |
| topic_facet | Integration, Functional Funktionalintegration |
| url | https://doi.org/10.1017/CBO9780511535062 |
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