Quantization on the Torus and modular invariance
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Knowledge AreaMatemática Aplicada
SponsorsJ. Guerrero thanks the Spanish MEC for a Postdoctoral grant and the Department of Physics of Naples-INFN for its hospitality and financial support, and M. Calixto thanks the Spanish MEC for a FPI grant. Work partially supported by the DGICYT.
Bibliographic CitationGUERRERO GARCÍA, Julio, CALIXTO MOLINA, Manuel, ALDAYA VALVERDE, Victor. Quantization on the Torus and modular invariance. En: International Colloquium on Group Theoretical Methods in Physics (21º : 1996: Goslar). Goslar: 1999, 24p.
Teoría de Abelian Chern-Simons
The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a group-theoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is even, or antiperiodic if n is odd. If the symplectic form is of rational cohomology class n/r , a similar result holds –the wave functions must be either periodic or antiperiodic on a torus r times larger in both direccions, depending on the parity of nr. Application of these results to the Abelian Chern-Simons is discussed.
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