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Functional integration : = action and symmetries /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Functional integration :/ Pierre Cartier and Cé́́cile DeWitt-Morette.
Reminder of title:	action and symmetries /
Author:	Cartier, Pierre,
other author:	DeWitt-Morette, Cécile,
Description:	1 online resource (xx, 456 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Integration, Functional. -
Online resource:	https://doi.org/10.1017/CBO9780511535062
ISBN:	9780511535062 (ebook)

Functional integration : = action and symmetries /
Cartier, Pierre,

Functional integration :action and symmetries /Pierre Cartier and Cé́́cile DeWitt-Morette. - 1 online resource (xx, 456 pages) :digital, PDF file(s). - Cambridge monographs on mathematical physics. - 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.

ISBN: 9780511535062 (ebook)Subjects--Topical Terms:

684226
Integration, Functional.

LC Class. No.: QC20.7.F85 / C376 2006

Dewey Class. No.: 530.1557

Functional integration : = action and symmetries /
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505 0 $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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