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Title: Wave Packet Analysis of Feynman Path Integrals ([EBook]) / Fabio Nicola , S. Ivan Trapasso Dewey Class: 530.1430151543 Author: Nicola, Fabio Added Personal Name: Trapasso, S. Ivan Publication: Cham : Springer International Publishing, 2022 Physical Details: : online resource (xiii, 214 p.) Series: Lecture notes in mathematics.; 2305 ISBN: 9783031061868 Mode of acces to digital resource: Digital reproduction.-Cham :Springer International Publishing,2022. -Digital book. Cham Springer Nature 2022. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format System details note: Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). Summary Note: 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.: ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
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