TY  - GEN
AB  - 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.
AU  - Nicola, Fabio.
AU  - Trapasso, S. Ivan.
CN  - QC174.17.F45
CY  - Cham, Switzerland :
DA  - 2022.
DO  - 10.1007/978-3-031-06186-8
DO  - doi
ID  - 1448473
KW  - Quantum theory.
KW  - Feynman integrals.
KW  - Gabor transforms.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-06186-8
N2  - 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.
PB  - Springer,
PP  - Cham, Switzerland :
PY  - 2022.
SN  - 9783031061868
SN  - 3031061861
T1  - Wave packet analysis of Feynman path integrals/
TI  - Wave packet analysis of Feynman path integrals/
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-06186-8
VL  - v. 2305
ER  -