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Table of contents (10 chapters)
Keywords
About this book
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory.
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Reviews
From the reviews of the second edition:
"The second edition (from 2008) contains a large additional chapter … entitled ‘Some Recent Developments’, where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration." (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)
“The new edition goes way beyond the habitual corrections and additions … . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals.” (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Mathematical Theory of Feynman Path Integrals
Book Subtitle: An Introduction
Authors: Sergio A. Albeverio, Raphael J. Høegh-Krohn, Sonia Mazzucchi
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-76956-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-76954-5Published: 30 May 2008
eBook ISBN: 978-3-540-76956-9Published: 06 May 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 2
Number of Pages: X, 182
Additional Information: Authors of the 1st edition: Sergio A. Albeverio, Raphael J. Høegh-Krohn
Topics: Integral Equations, Measure and Integration, Functional Analysis, Operator Theory, Probability Theory and Stochastic Processes, Global Analysis and Analysis on Manifolds