Quantum Mechanics Over a q-DEFORMED (0 + 1)-DIMENSIONAL Superspace

We built up an explicit realization of (0 + 1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and a q-supersymmetric action. We consider a functional integral based on this action. Integration is implemented, at the level of the coordinates and at the level of the fields, as traces over the corresponding representation spaces. Evaluation of these traces leads us to standard functional integrals. The generation of a mass term for the fermion field leads, at this level, to an explicitly broken version of supersymmetric quantum mechanics.