1995/02/08 by Sardanashvily, G.
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.gr-qc/9502022
In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold X. 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 X by the Lorentz group. The key point lies in the fact that different tetrad fields imply nonequivalent representations of cotangent vectors to X 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→\Si→ X where values of tetrad fields play the role of parameter coordinates, besides the familiar world coordinates.