Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambigui...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1995 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/24569 |
| Acceso en línea: | https://hdl.handle.net/2445/24569 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria de grups Camps de galga (Física) Teoria quàntica Group theory Gauge fields (Physics) Quantum theory |
| Sumario: | A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics. |
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