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...

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Detalles Bibliográficos
Autores: Aldaya Valverde, Víctor, Guerrero García, Julio, Calixto Molina, Manuel
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
Descripción
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.