Advances in Applied Clifford Algebras

, Volume 21, Issue 4, pp 677–696 | Cite as

Operator Identities in q-Deformed Clifford Analysis

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Abstract

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 \({\mathbb{R}^m}\), for which the q-Dirac operator satisfies Stokes’ formula, is defined. The orthogonal q-Clifford- Hermite polynomials for this integration are briefly studied.

Keywords

q-derivative Dirac operator radial algebra 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.GentBelgium

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