Phase space method for the Euclidean motion group: The fundamental formula

The objective of this work is to present some aspects of the phase space representation of quantum mechanics on the Euclidean Motion Group of rank three. In particular, the main contribution of this paper is the statement and proof of fundamental formula relating the Weyl transform for the group and...

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Main Authors:	Natividad, Laarni B, Nable, Job A
Format:	text
Published:	Archīum Ateneo 2022
Subjects:	Mathematics Physical Sciences and Mathematics Physics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/220 https://doi.org/10.1063/5.0092901
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1221
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spelling	ph-ateneo-arc.mathematics-faculty-pubs-12212022-12-06T05:47:44Z Phase space method for the Euclidean motion group: The fundamental formula Natividad, Laarni B Nable, Job A The objective of this work is to present some aspects of the phase space representation of quantum mechanics on the Euclidean Motion Group of rank three. In particular, the main contribution of this paper is the statement and proof of fundamental formula relating the Weyl transform for the group and the Wigner functions on the group, given by F1\|WkF2 =R3so(3)k(c,C)WE(3)(F1,F2)dc dC. Here, Wk is the Weyl transform of the function k on E(3) and WE(3) is the Wigner transform. Thus, the various phase space objects such as the Wigner transform and the Weyl transform are also explicitly formulated on the Euclidean Motion Group. 2022-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/220 https://doi.org/10.1063/5.0092901 Mathematics Faculty Publications Archīum Ateneo Mathematics Physical Sciences and Mathematics Physics
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	Mathematics Physical Sciences and Mathematics Physics
spellingShingle	Mathematics Physical Sciences and Mathematics Physics Natividad, Laarni B Nable, Job A Phase space method for the Euclidean motion group: The fundamental formula
description	The objective of this work is to present some aspects of the phase space representation of quantum mechanics on the Euclidean Motion Group of rank three. In particular, the main contribution of this paper is the statement and proof of fundamental formula relating the Weyl transform for the group and the Wigner functions on the group, given by F1\|WkF2 =R3so(3)k(c,C)WE(3)(F1,F2)dc dC. Here, Wk is the Weyl transform of the function k on E(3) and WE(3) is the Wigner transform. Thus, the various phase space objects such as the Wigner transform and the Weyl transform are also explicitly formulated on the Euclidean Motion Group.
format	text
author	Natividad, Laarni B Nable, Job A
author_facet	Natividad, Laarni B Nable, Job A
author_sort	Natividad, Laarni B
title	Phase space method for the Euclidean motion group: The fundamental formula
title_short	Phase space method for the Euclidean motion group: The fundamental formula
title_full	Phase space method for the Euclidean motion group: The fundamental formula
title_fullStr	Phase space method for the Euclidean motion group: The fundamental formula
title_full_unstemmed	Phase space method for the Euclidean motion group: The fundamental formula
title_sort	phase space method for the euclidean motion group: the fundamental formula
publisher	Archīum Ateneo
publishDate	2022
url	https://archium.ateneo.edu/mathematics-faculty-pubs/220 https://doi.org/10.1063/5.0092901
_version_	1751550496765640704

Phase space method for the Euclidean motion group: The fundamental formula

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