Operator Identities in q-Deformed Clifford Analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on mathbbR^m{mathbb{R}^m}, for which the q-Dirac operator satisfies Stokes’ formula, is defined. The orthogonal q-Clifford- Hermite polynomials for this integration are briefly studied.