On an inductive construction of higher spin Dirac operators

In this contribution, we introduce higher spin Dirac operators, i.e. a specific class of differential operators in Clifford analysis of several vector variables, motivated by equations from theoretical physics. In particular, the higher spin Dirac operator in three vector variables will be explicitly constructed, starting from a description of the so-called twisted Rarita-Schwinger operator

On the harmonic and monogenic decomposition of polynomials

The decomposition of polynomials in terms of spherical harmonics is widely used in various branches of analysis. In this paper we describe a set of REDUCE procedures generating this decomposition and its more general, monogenic, counterpart in Clifford analysis. We then illustrate their use by inverting the Laplacian and the Dirac operator on both Euclidean and Minkowski spaces