SU(2) particle sigma model: The role of contact symmetries in global quantization
In this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S , by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-in...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/384399 |
| Acceso en línea: | http://hdl.handle.net/10261/384399 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlinear systems Sigma model Contact symmetries Non-canonical quantization Non trivial topology |
| Sumario: | In this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S , by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-invariant at the classical level, although not necessarily the Lagrangian. Special attention is paid to the role played by the basic quantum commutators, which depart from the canonical, Heisenberg-Weyl ones, as well as the relationship between the integration measure in the Hilbert space of the system and the non-trivial topology of the configuration space. Also, the quantization on momentum space is briefly outlined. © 2016 IOP Publishing Ltd. |
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