Dispersion Operators Algebra and Linear Canonical Transformations

TL;DR

This paper explores the mathematical relationships between dispersion operators algebra, linear canonical transformations, and phase space representations in quantum mechanics, providing a multidimensional generalization of these concepts.

Contribution

It introduces a new framework linking dispersion operators algebra with linear canonical transformations within phase space quantum mechanics, extending previous results to multiple dimensions.

Findings

Established a connection between dispersion operators algebra and linear canonical transformations.

Developed a multidimensional generalization of the algebra and transformations.

Provided insights into phase space representations of quantum mechanics.

Abstract

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given