Symbol Correspondence for Euclidean Systems
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....
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| Format: | text |
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Archīum Ateneo
2021
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/192 https://projecteuclid.org/journals/journal-of-geometry-and-symmetry-in-physics/volume-62/issue-none/Symbol-Correspondence-for-Euclidean-Systems/10.7546/jgsp-62-2021-67-84.short?tab=ArticleLink |
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| Institution: | Ateneo De Manila University |
| Summary: | 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. |
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