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
Format:	text
Published:	Archīum Ateneo 2021
Subjects:	Euclidean motion group Moyal star-product unitary representations Weyl transform Wigner function Mathematics
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

id	ph-ateneo-arc.mathematics-faculty-pubs-1201
record_format	eprints
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
_version_	1731309308431302656

Symbol Correspondence for Euclidean Systems

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