Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept

We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of continuity in the analytic foundations of Wigner’s...

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Main Authors:	Julio Marny Hoff da Silva, Gabriel Marcondes Caires da Rocha
Format:	Article
Language:	English
Published:	MDPI AG 2021-08-01
Series:	Universe
Subjects:	ray representation strongly continuous continuity Hilbert space
Online Access:	https://www.mdpi.com/2218-1997/7/8/285

id	doaj-30d41f90225146b4af590fcb1aa93509
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spelling	doaj-30d41f90225146b4af590fcb1aa935092021-08-26T14:25:21ZengMDPI AGUniverse2218-19972021-08-01728528510.3390/universe7080285Strongly Continuous Representations in the Hilbert Space: A Far-Reaching ConceptJulio Marny Hoff da Silva0Gabriel Marcondes Caires da Rocha1Department of Physics, UNESP, Estadual Paulista University, 12516-410 Brazilia, BrazilDepartment of Physics, UNESP, Estadual Paulista University, 12516-410 Brazilia, BrazilWe revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of continuity in the analytic foundations of Wigner’s work. We conclude the paper by reviewing the connection between continuity, the possibility of defining certain local groups, and their relation to projective representations.https://www.mdpi.com/2218-1997/7/8/285ray representationstrongly continuouscontinuityHilbert space
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Julio Marny Hoff da Silva Gabriel Marcondes Caires da Rocha
spellingShingle	Julio Marny Hoff da Silva Gabriel Marcondes Caires da Rocha Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept Universe ray representation strongly continuous continuity Hilbert space
author_facet	Julio Marny Hoff da Silva Gabriel Marcondes Caires da Rocha
author_sort	Julio Marny Hoff da Silva
title	Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept
title_short	Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept
title_full	Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept
title_fullStr	Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept
title_full_unstemmed	Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept
title_sort	strongly continuous representations in the hilbert space: a far-reaching concept
publisher	MDPI AG
series	Universe
issn	2218-1997
publishDate	2021-08-01
description	We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of continuity in the analytic foundations of Wigner’s work. We conclude the paper by reviewing the connection between continuity, the possibility of defining certain local groups, and their relation to projective representations.
topic	ray representation strongly continuous continuity Hilbert space
url	https://www.mdpi.com/2218-1997/7/8/285
work_keys_str_mv	AT juliomarnyhoffdasilva stronglycontinuousrepresentationsinthehilbertspaceafarreachingconcept AT gabrielmarcondescairesdarocha stronglycontinuousrepresentationsinthehilbertspaceafarreachingconcept
_version_	1721189568070287360

Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept

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