Rarita–Schwinger Type Operators in Clifford Analysis

In this paper we investigate a generalization of the classical Rarita–Schwinger equations for spin 3/2 fields to the case of functions taking values in irreducible representation spaces with weight k+1/2. These fields may be realised as functions taking values in spaces of spherical monogenics earlier considered in F. Sommen and N. Van Acker (1993, in “Clifford Algebras and Their Applications in Mathematical Physics,” Kluwer Academic, Dordrecht/Norwell, MA). In this paper we develop the main function theoretic results.