Format:
1 Online-Ressource (xiii, 214 Seiten)
ISBN:
9783031061868
Series Statement:
Lecture Notes in Mathematics volume 2305
Content:
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.
Additional Edition:
ISBN 9783031061851
Additional Edition:
Erscheint auch als Druck-Ausgabe Nicola, Fabio Wave packet analysis of Feynman path integrals Cham, Switzerland : Springer, 2022 ISBN 9783031061851
Language:
English
Keywords:
Gabor-Transformation
;
Pfadintegral
;
Wellenpaket
;
Zeit-Frequenz-Analyse
;
Kurzzeit-Fourier-Transformation
DOI:
10.1007/978-3-031-06186-8
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