Group averaging and the Ashtekar-Horowitz model
We investigate refined algebraic quantisation of the constrained Hamiltonian system known as the Ashtekar-Horowitz model. We study twoversions of this model which are defined on a two-torus and on a cylinder, respectively. The dimension of the physical Hilbert space dependson the topological structu...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2007 |
| País: | México |
| Recursos: | Universidad de Colima |
| Repositório: | Redalyc-UCOL |
| OAI Identifier: | oai:redalyc.org:57066421 |
| Acesso em linha: | https://www.redalyc.org/articulo.oa?id=57066421 https://www.redalyc.org/journal/570/57066421/ https://www.redalyc.org/journal/570/57066421/html/ https://www.redalyc.org/journal/570/57066421/57066421.epub https://www.redalyc.org/journal/570/57066421/movil |
| Access Level: | Acceso aberto |
| Palavra-chave: | Física, Astronomía y Matemáticas Group averaging constrained systems superselection sectors |
| Resumo: | We investigate refined algebraic quantisation of the constrained Hamiltonian system known as the Ashtekar-Horowitz model. We study twoversions of this model which are defined on a two-torus and on a cylinder, respectively. The dimension of the physical Hilbert space dependson the topological structure of the model. In particular, we see that for the compact version of the model the representation of the physicalobservable algebra is irreducible for generic potentials but decomposes into irreducible subrepresentations for certain special potentials. Thesuperselection sectors are related to singularities in the reduced phase space and to the rate of divergence in the formal group averagingintegral. For both versions, there is no tunnelling into the classically forbidden region of the unreduced configuration space. |
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