%0 Journal Article 
%A Guerrero García, Julio
%A Aldaya Valverde, Víctor
%A Calixto Molina, Manuel
%T Quantization on the Torus and modular invariance
%D 1999
%U http://hdl.handle.net/10317/526
%U arXiv:hep-th/9707237v2
%X 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.
%K Matemática Aplicada
%K Cuantización
%K Torus
%K Teoría de Abelian Chern-Simons
%K Cohomología
%~ GOEDOC, SUB GOETTINGEN