Composite Spinor Bundles in Gravitation Theory
arXiv:gr-qc/9502022
Abstract
In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold . In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between these spinor bundles and the tetrad gravitational fields represented by sections of the quotient $\Si$ of the linear frame bundle over by the Lorentz group. The key point lies in the fact that different tetrad fields imply nonequivalent representations of cotangent vectors to by the Dirac's matrices. It follows that a fermion field must be regarded only in a pair with a certain tetrad field. These pairs can be represented by sections of the composite spinor bundle $S\to\Si\to X$ where values of tetrad fields play the role of parameter coordinates, besides the familiar world coordinates.
26 pp, LaTeX file