On the existence of the second Dirac operator in Riemannian space
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In this article, the second Dirac operator is shown to be equivalent to a standard Dirac one in Riemannian spaces with a five-dimensional motion group, and it is shown that it exists in all metrics for which it exists.Abstract:
We describe a Riemannian space class where the second Dirac operator arises and prove that the operator is always equivalent to a standard Dirac one. The particle state in this gravitational field is degenerate to some extent and we introduce an additional value in order to describe a particle state completely. Some supersymmetry constructions are also discussed. As an example we study all Riemannian spaces with a five-dimensional motion group and find all metrics for which the second Dirac operator exists. On the basis of our discussed examples we hypothesize about the number of second Dirac operators in Riemannian space.read more
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W. Dietz,R. Rudiger +1 more
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