Darboux, Moser and Weinstein theorems for prequantum systems

We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symple...

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Detalhes bibliográficos
Autores: Miranda Galcerán, Eva|||0000-0001-9518-5279, Weitsman, Jonathan
Formato: informe técnico
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/414761
Acesso em linha:https://hdl.handle.net/2117/414761
https://dx.doi.org/10.48550/arXiv.2404.04988
Access Level:acceso abierto
Palavra-chave:Classificació AMS::81 Quantum theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descrição
Resumo:We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symplectomorphism and a gauge transformation. As an application, we show that the Bohr-Sommerfeld quantization of prequantum system on a manifold with trivial first cohomology is independent of the choice of the connection.