On the conjugate of the Dirac operator

Abstract

We analyse the behaviour of the Euclidean Dirac operator under a special transformation preserving monogenicity. The framework of Vahlen matrices (seeAhlfors, Maks) provides the tools for such a treatment. We show that the conjugate of the Dirac operator with respect to such a transformation leads to a first order operator on a Riemannian manifold with a weighed metric and present some properties of such an operator. An explicit construction is done, using the Cayley transformation.