Interaction of Massless Dirac Field with a Poincare Gauge Field

Abstract

In this paper we consider a model of Poincaré gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einstein's gravitational field and a pair of "Yang-Mills" field and its partner, respectively. In this model we re-derive some special solutions and take up one of them. The solution represents a "Yang-Mills" field without its partner field and the Reissner-Nordström type spacetime, which are generated by a PGT-gauge charge and its mass. It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the "Yang-Mills" field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordström geometry. The difference between left-and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordström type black-hole. 04.50.+h, 04.25.Nx