Mathematical Theory of Feynman Path Integrals

An Introduction
Buch | Softcover
X, 182 Seiten
2008 | 2nd, corr. and enlarged ed. 2008
Springer Berlin (Verlag)
978-3-540-76954-5 (ISBN)

Lese- und Medienproben

Mathematical Theory of Feynman Path Integrals - Sergio Albeverio, Rafael Høegh-Krohn, Sonia Mazzucchi
42,79 inkl. MwSt

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.

Preface to the second edition.- Preface to the first edition.- 1.Introduction.- 2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa.- 3.The Feynman Path Integral in Potential Scattering.- 4.The Fresnel Integral Relative to a Non-singular Quadratic Form.- 5.Feynman Path Integrals for the Anharmonic Oscillator.- 6.Expectations with Respect to the Ground State of the Harmonic Oscillator.- 7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- 8.The Invariant Quasi-free States.- 9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field.- 10.Some Recent Developments.- 10.1.The infinite dimensional oscillatory integral.- 10.2.Feynman path integrals for polynomially growing potentials.- 10.3.The semiclassical expansio.- 10.4.Alternative approaches to Feynman path integrals.- 10.4.1.Analytic continuation.- 10.4.2.White noise calculus.- 10.5.Recent applications.- 10.5.1.The Schroedinger equation with magnetic fields.- 10.5.2.The Schroedinger equation with time dependent potentials.- 10.5.3 .hase space Feynman path integrals.- 10.5.4.The stochastic Schroedinger equation.- 10.5.5.The Chern-Simons functional integral.- References of the first edition.- References of the second edition.- Analytic index.- List of Notations.

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)

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)

Erscheint lt. Verlag 30.5.2008
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo X, 182 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 286 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte 81Q30, 81S40, 28C20, 46Nxx, 46T12, 47D08, 47G30, 60H05, 58D3 • Calculus • Feynman path integrals • Geometry • (infinite dimensional) oscillatory integrals • Mechanics • Number Theory • Potential • quantum mechanics • quantum theory of fields • semiclassical asymptotic expansions
ISBN-10 3-540-76954-4 / 3540769544
ISBN-13 978-3-540-76954-5 / 9783540769545
Zustand Neuware
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