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2021 Symbol Correspondence for Euclidean Systems
Laarni B. Natividad, Job A. Nable
J. Geom. Symmetry Phys. 62: 67-84 (2021). DOI: 10.7546/jgsp-62-2021-67-84

Abstract

The three main objects that serve as the foundation of quantum mechanics on phase space are the Weyl transform, the Wigner distribution function, and the $\star$-product of phase space functions.

In this article, the $\star$-product of functions on the Euclidean motion group of rank three, $\mathrm{E}(3)$, is constructed. $C^*$-algebra properties of $\star_s$ on $\mathrm{E}(3)$ are presented, establishing a phase space symbol calculus for functions whose parameters are translations and rotations. The key ingredients in the construction are the unitary irreducible representations of the group.

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Laarni B. Natividad. Job A. Nable. "Symbol Correspondence for Euclidean Systems." J. Geom. Symmetry Phys. 62 67 - 84, 2021. https://doi.org/10.7546/jgsp-62-2021-67-84

Information

Published: 2021
First available in Project Euclid: 4 February 2022

Digital Object Identifier: 10.7546/jgsp-62-2021-67-84

Rights: Copyright © 2021 Bulgarian Academy of Sciences, Institute of Mechanics

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