Wave packet analysis of Feynman path integrals
Author(s)
Bibliographic Information
Wave packet analysis of Feynman path integrals
(Lecture notes in mathematics, 2305)
Springer, 2022
- : pbk
Available at 27 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Science and Technology Library, Kyushu University
: pbkSER/LNM/2305130012022005293,
SER/LNM/2305130012022005293 -
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkL/N||LNM||2305200043575306
Note
Includes bibliographical references (p. 199-208) and index
Description and Table of Contents
Description
The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schroedinger-type evolution equation) involving a suitably designed sequence of operators.
In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets - can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction.
This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.
Table of Contents
- Itinerary - How Gabor Analysis met Feynman Path Integrals.
- Part I Elements of Gabor Analysis.
- Basic Facts of Classical Analysis. - The Gabor Analysis of Functions. - The Gabor Analysis of Operators. - Semiclassical Gabor Analysis.
- Part II Analysis of Feynman Path Integrals.
- Pointwise Convergence of the Integral Kernels. - Convergence in L(L2) - Potentials in the Sjoestrand Class. - Convergence in L(L2) - Potentials in Kato-Sobolev Spaces. - Convergence in the Lp Setting.
by "Nielsen BookData"