Abbildung von Nicola / Trapasso | Wave Packet Analysis of Feynman Path Integrals | 1. Auflage | 2022 | 2305 |

Nicola / Trapasso

Wave Packet Analysis of Feynman Path Integrals

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Buch. Softcover

1st ed. 2022. 2022

xiii, 214 S. 3 Farbabbildungen, 3 Farbtabellen, Bibliographien.

In englischer Sprache

Springer. ISBN 978-3-031-06185-1

Format (B x L): 15,5 x 23,5 cm

Gewicht: 355 g

Das Werk ist Teil der Reihe: Lecture Notes in Mathematics; 2305


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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