Group averaging and the Ashtekar-Horowitz model
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| Format: | Artículo científico |
| Language: | en |
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Sociedad Mexicana de Física A.C.
2007
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| _version_ | 1876464766394826752 |
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| author | Alberto Molgado |
| author_facet | Alberto Molgado |
| contents | Group averaging and the Ashtekar-Horowitz model Alberto Molgado Física, Astronomía y Matemáticas Group averaging constrained systems superselection sectors 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. 2007 artículo científico 0035-001X 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 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.4 Vol.53 |
| format | Artículo científico |
| id | redalyc_57066421 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Group averaging and the Ashtekar-Horowitz model Alberto Molgado Física, Astronomía y Matemáticas Group averaging constrained systems superselection sectors Group averaging and the Ashtekar-Horowitz model Alberto Molgado Física, Astronomía y Matemáticas Group averaging constrained systems superselection sectors 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. 2007 artículo científico 0035-001X 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 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.4 Vol.53 |
| title | Group averaging and the Ashtekar-Horowitz model |
| topic | Física, Astronomía y Matemáticas Group averaging constrained systems superselection sectors |
| url | 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 |