Interaction of Massless Dirac Field with a Poincare Gauge Field

In this paper we consider a model of Poincar\'e gauge theory (PGT) in which atranslational gauge field and a Lorentz gauge field are actually identifiedwith the Einstein's gravitational field and a pair of ``Yang-Mills'' field andits partner, respectively.In this model we re-derive some special solutions andtake up one of them. The solution represents a ``Yang-Mills'' field without itspartner field and the Reissner-Nordstr\"om type spacetime, which are generatedby a PGT-gauge charge and its mass.It is main purpose of this paper toinvestigate the interaction of massless Dirac fields with those fields. As aresult, we find an interesting fact that the left-handed massless Dirac fieldsbehave in the different manner from the right-handed ones. This can beexplained as to be caused by the direct interaction of Dirac fields with the``Yang-Mills'' field. Accordingly, the phenomenon can not happen in thebehavior of the neutrino waves in ordinary Reissner-Nordstr\"om geometry. Thedifference between left- and right-handed effects is calculated quantitatively,considering the scattering problems of the massless Dirac fields by ourReissner-Nordstr\"om type black-hole.Comment: 10pages, RevTeX3.