TY - JOUR A1 - Aldaya Valverde, Víctor AU - Guerrero García, Julio AU - Calixto Molina, Manuel T1 - Algebraic Quantization, Good Operators and Fractional Quantum Numbers Y1 - 1995 SN - 0010-3616 UR - http://hdl.handle.net/10317/522 UR - arXiv:hep-th/9507016v4 AB - 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. KW - Matemática Aplicada KW - Cuantización algebraica KW - Cuántica de números fraccionados LA - eng PB - Springer Berlin ER -