Dirac-Hestenes spinor fields on Riemann-Cartan manifolds (Q674891)

The authors study Dirac-Hestenes spinor fields on a 4-dimensional Riemann-Cartan spacetime, and show that they are defined by certain equivalence classes of even sections of a Clifford bundle over the spacetime. This new bundle is called a spin Clifford bundle, and the conditions for its existence are shown to be equivalent to those given in Geroch's theorem for the existence of a spinor structure on a Lorentzian spacetime. The notions of covariant and algebraic Dirac spinor fields are introduced and compared with Dirac-Hestenes spinor fields. It is shown that all three kinds of spinor fields contain the same mathematical and physical information, and likewise Crumeyrolle's notion of amorphous spinors is clarified. A covariant derivative of Clifford fields and Dirac-Hestenes spinor fields is constructed, and by use of a variational principle a procedure for generalizing the Dirac-Hestenes equation from a Minkowskian spacetime to a Riemann-Cartain spacetime is exhibited. Contents include: an introduction; covariant, algebraic, and Dirac-Hestenes spinors; the Clifford bundle of spacetime and its irreducible module representations; covariant derivatives of Clifford and Dirac-Hestenes spinor fields; the form derivative of the manifold and the Dirac and spin-Dirac operators; the Dirac-Hestenes equation in a Minkowskian spacetime; a Lagrangian formalism for the Dirac-Hestenes spinor field on a Riemann-Cartan spacetime; and conclusions.