The York Research Database

In the method of q-Borel quantization, quantum observables - that is, self-adjoint operators in a suitably chosen Hilbert space - can be assigned a particular set of q-deformed position and momentum observables. In this pattern, the momentum operator appears to be a q-difference operator - and not a differential operator - so that the result is useful in modeling quantum mechanics over discrete configuration spaces. q-Borel quantization was introduced for special cases in which classical observables are modeled over the configuration space S. Here, a generalization of the formalism to n-dimensional torus T is discussed.