Wave packet analysis of Feynman path integrals / Fabio Nicola, S. Ivan Trapasso.

Format:

Book

Author/Creator:

Nicola, Fabio, author.

Trapasso, S. Ivan, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2305.

Lecture Notes in Mathematics, 0075-8434 ; Volume 2305

Language:

English

Subjects (All):

Quantum theory.

Wave packets.

Feynman integrals.

Gabor transforms.

Physical Description:

xiii, 211 pages : color illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer Nature Switzerland AG, [2022]

Summary:

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 Schrodinger-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.

Notes:

Includes bibliographical references (pages 199-208) and index.

Current copyright fee: GBP19.00 42\0.

Other Format:

Online version: Nicola, Fabio. Wave packet analysis of Feynman path integrals.

ISBN:

9783031061851

3031061853

OCLC:

1338681349