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 , for which the q -Dirac operator satisfies Stokes’ formula, is defined. The orthogonal q -Clifford- Hermite polynomials for this integration are briefly studied.