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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Main Authors: Natividad, Laarni B, Nable, Job A
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出版: Archīum Ateneo 2021
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在線閱讀: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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spelling 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
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection 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
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