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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Archīum Ateneo
2021
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| الوصول للمادة أونلاين: | 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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ph-ateneo-arc.mathematics-faculty-pubs-12012022-04-21T06:53:59Z Symbol Correspondence for Euclidean Systems Natividad, Laarni B Nable, Job A 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. 2021-01-01T08:00:00Z text 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 Mathematics Faculty Publications Archīum Ateneo Euclidean motion group Moyal star-product unitary representations Weyl transform Wigner function Mathematics |
| institution |
Ateneo De Manila University |
| building |
Ateneo De Manila University Library |
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Asia |
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Philippines Philippines |
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Ateneo De Manila University Library |
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archium.Ateneo Institutional Repository |
| topic |
Euclidean motion group Moyal star-product unitary representations Weyl transform Wigner function Mathematics |
| spellingShingle |
Euclidean motion group Moyal star-product unitary representations Weyl transform Wigner function Mathematics Natividad, Laarni B Nable, Job A Symbol Correspondence for Euclidean Systems |
| description |
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. |
| format |
text |
| author |
Natividad, Laarni B Nable, Job A |
| author_facet |
Natividad, Laarni B Nable, Job A |
| author_sort |
Natividad, Laarni B |
| title |
Symbol Correspondence for Euclidean Systems |
| title_short |
Symbol Correspondence for Euclidean Systems |
| title_full |
Symbol Correspondence for Euclidean Systems |
| title_fullStr |
Symbol Correspondence for Euclidean Systems |
| title_full_unstemmed |
Symbol Correspondence for Euclidean Systems |
| title_sort |
symbol correspondence for euclidean systems |
| publisher |
Archīum Ateneo |
| publishDate |
2021 |
| url |
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 |
| _version_ |
1731309308431302656 |