Nonlocalized field theory over spinor bundles: Poincaré gravity and Yang-Mills fields

In this paper we study the differential structure of a spinor bundle in spaces where the metric tensor gμν(x, ξ, \̄gx) of the base manifold depends on the position x as well as on the spinor variables ξ and \̄gx. Notions such as: gauge covariant derivatives of tensors, connections, curvatures, torsions and Bianchi identities are presented in the context of a gauge approach, different than the one proposed in [11, 13], due to the introduction of a Poincaré group and the use of d-connections [6, 8] in the spinor bundle S(2) M. The introduction of basic 1-form fields ϱμ and spinors ζa, \̄gza with values in the Lie algebra of the Poincaré group is also essential in our study. The gauge field equations are derived by the authors [12]. Finally, we give the Yang-Mills and the Yang-Mills-Higgs equations in a form sufficiently generalized for our approach.