On the existence of the second Dirac operator in Riemannian space

Details On the existence of the second Dirac operator in Riemannian space On the existence of the second Dirac operator in Riemannian space

2000-04-24

arxiv.org/abs/hep-th/0004161v1

Class.Quant.Grav. 17 (2000) 305-318

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 10 pages, no figures

Scientific paper

10.1088/0264-9381/17/2/303

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-dimentional 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.

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