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Wave packet analysis of Feynman path integrals

Record Type:	Electronic resources : Monograph/item
Title/Author:	Wave packet analysis of Feynman path integralsby Fabio Nicola, S. Ivan Trapasso.
Author:	Nicola, Fabio.
other author:	Trapasso, S. Ivan.
Published:	Cham :Springer International Publishing :2022.
Description:	xiii, 214 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Quantum theory.
Online resource:	https://doi.org/10.1007/978-3-031-06186-8
ISBN:	9783031061868$q(electronic bk.)

Wave packet analysis of Feynman path integrals
Nicola, Fabio.

Wave packet analysis of Feynman path integrals[electronic resource] /by Fabio Nicola, S. Ivan Trapasso. - Cham :Springer International Publishing :2022. - xiii, 214 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23051617-9692 ;. - Lecture notes in mathematics ;2035..

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 Schrödinger-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.

ISBN: 9783031061868$q(electronic bk.)

Standard No.: 10.1007/978-3-031-06186-8doiSubjects--Topical Terms:

199020
Quantum theory.

LC Class. No.: QC174.17.F45 / N53 2022

Dewey Class. No.: 530.12

Wave packet analysis of Feynman path integrals
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520 $a 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 Schrödinger-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.
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