DIRAC-HESTENES SPINOR FIELDS ON RIEMANN-CARTAN MANIFOLDS

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-d imensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of th e Clifford bundle (over the RCST), thereby being certain particular se ctions of a new bundle named the spin-Clifford bundle (SCB). The condi tions for the existence of the SCB are studied and are shown to be equ ivalent to Geroch's theorem concerning the existence of spinor structu res in a Lorentzian spacetime. We introduce also the covariant and alg ebraic Dirac spinor fields and compare these with DHSF, showing that a ll three kinds of spinor fields contain the same mathematical and phys ical information. We clarify also the notion of (Crumeyrolle's) amorph ous spinors (Dirac-Kahler spinor fields are of this type), showing tha t they cannot be used to describe fermionic fields. We develop a rigor ous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We sh ow how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a varia tional principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.