Algebraic Quantization, Good Operators and Fractional Quantum Numbers
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the “failure” of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of “constrained” Heisenb...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1995 |
| País: | España |
| Institución: | Universidad Politécnica de Cartagena(UPCT) |
| Repositorio: | Repositorio Digital UPCT |
| OAI Identifier: | oai:repositorio.upct.es:10317/522 |
| Acceso en línea: | http://hdl.handle.net/10317/522 |
| Access Level: | acceso abierto |
| Palabra clave: | Cuantización algebraica Cuántica de números fraccionados Matemática Aplicada |
| Sumario: | The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the “failure” of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of “constrained” Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring “anomalous” operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively. |
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