Dispersion Operators Algebra and Linear Canonical Transformations

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

13 pages

References in corpus (2)

• A Top-Down Account of Linear Canonical Transforms
• Quantum Mechanics in Phase Space

Cited by in corpus (6)

• Linear Canonical Transformations in Relativistic Quantum Physics
• Invariant quadratic operators associated with Linear Canonical Transformations and their eigenstates
• Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach
• Sterile neutrinos existence suggested from LCT covariance
• Properties of Elementary Fermions of the Standard Model deduced from Linear Canonical Transformations
• Study on a Spinorial Representation of Linear Canonical Transformations