Symbol Correspondence for Euclidean Systems
Document Type
Article
Publication Date
2021
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 ⋆-product of phase space functions.
In this article, the ⋆-product of functions on the Euclidean motion group of rank three, E(3), is constructed. C ∗ -algebra properties of ⋆s on 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.
Recommended Citation
Natividad, L. B., & Nable, J. A. (2021). Symbol correspondence for Euclidean Systems. Journal of Geometry and Symmetry in Physics, 62, 67–84. https://doi.org/10.7546/jgsp-62-2021-67-84
