Wave Packet Analysis of Feynman Path Integrals

Wave Packet Analysis of Feynman Path Integrals（Lecture Notes in Mathematics）

费曼路径积分的波包分析
理论物理学

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作者

Nicola

出版社

Springer Berlin Heidelberg

出版时间

2022年07月30日

装帧

平装

ＩＳＢＮ

9783031061851

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页码

230

语种

英文

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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.

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 Sjöstrand Class.- Convergence in L(L2) - Potentials in Kato-Sobolev Spaces.- Convergence in the Lp Setting.

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