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...
| Autores: | , |
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| 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 |
| 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. |
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