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Rarita-Schwinger type operators in Clifford analysis. (English) Zbl 1078.30041

Summary: 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, Clifford algebras and their applications in mathematical physics. Proceedings of the third conference held at Deinze, Belgium, 1993. Dordrecht: Kluwer Academic Publishers. Fundam. Theor. Phys. 55, 203–212 (1993; Zbl 0840.30029)]. In this paper we develop the main function-theoretic results.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
15A66 Clifford algebras, spinors
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics

Citations:

Zbl 0840.30029
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References:

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