Enlargement of Symmetry Groups in Physics: A Practitioner’s Guide

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Autor(es): dc.contributorTransilvania University-
Autor(es): dc.contributorBabeș-Bolyai University-
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorWest University of Timișoara-
Autor(es): dc.contributorUniversité de Tours-
Autor(es): dc.creatorCsillag, Lehel-
Autor(es): dc.creatorHoff da Silva, Julio Marny-
Autor(es): dc.creatorPătuleanu, Tudor-
Data de aceite: dc.date.accessioned2025-08-21T20:02:59Z-
Data de disponibilização: dc.date.available2025-08-21T20:02:59Z-
Data de envio: dc.date.issued2025-04-29-
Data de envio: dc.date.issued2024-11-30-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.3390/universe10120448-
Fonte completa do material: dc.identifierhttps://hdl.handle.net/11449/298438-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/298438-
Descrição: dc.descriptionWigner’s classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to the theory of ordinary unitary representations by enlarging the group of physical symmetries. Nevertheless, the enlargement process is not always described explicitly: it is unclear in which cases the enlargement has to be conducted on the universal cover, a central extension, or a central extension of the universal cover. On the other hand, in the mathematical literature, projective unitary representations have been extensively studied, and famous theorems such as the theorems of Bargmann and Cassinelli have been achieved. The present article bridges the two: we provide a precise, step-by-step guide on describing projective unitary representations as unitary representations of the enlarged group. Particular focus is paid to the difference between algebraic and topological obstructions. To build the bridge mentioned above, we present a detailed review of the difference between group cohomology and Lie group cohomology. This culminates in classifying Lie group central extensions by smooth cocycles around the identity. Finally, the take-away message is a hands-on algorithm that takes the symmetry group of a given quantum theory as input and provides the enlarged group as output. This algorithm is applied to several cases of physical interest. We also briefly outline a generalization of Bargmann’s theory to time-dependent phases using Hilbert bundles.-
Descrição: dc.descriptionFaculty of Mathematics and Computer Science Transilvania University, Iuliu Maniu Street 50-
Descrição: dc.descriptionDepartment of Physics Babeș-Bolyai University, Kogălniceanu Street 1-
Descrição: dc.descriptionDepartamento de Física Universidade Estadual Paulista UNESP, Av. Dr. Ariberto Pereira da Cunha, 333, SP-
Descrição: dc.descriptionDepartment of Physics West University of Timișoara, Bd. Vasile Pârvan 4-
Descrição: dc.descriptionInstitut Denis Poisson UMR 7013 Université de Tours-
Descrição: dc.descriptionDepartamento de Física Universidade Estadual Paulista UNESP, Av. Dr. Ariberto Pereira da Cunha, 333, SP-
Idioma: dc.languageen-
Relação: dc.relationUniverse-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectcentral extension-
Palavras-chave: dc.subjectlifting problem-
Palavras-chave: dc.subjectprojective representation-
Palavras-chave: dc.subjectuniversal cover-
Título: dc.titleEnlargement of Symmetry Groups in Physics: A Practitioner’s Guide-
Tipo de arquivo: dc.typevídeo-
Aparece nas coleções:Repositório Institucional - Unesp

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