q-Borel quantization on S1 and Tn

The method of q-Borel quantization allows to assign to a particular set of q-deformed position and momentum observables corresponding quantum observables, i.e. self-adjoint operators in a suitably chosen Hilbert space. The latter have the property that the momentum operators is a q-difference operator instead of a differential operator, so that the result is useful to model quantum mechanics over discrete configuration space. q-Borel quantization has been introduced for the special case that the classical observables are modeled over the configuration space S1. Here, a generalization of the formalism to the n-dimensional Torus Tn is discussed