Composite Spinor Bundles in Gravitation Theory

Details Composite Spinor Bundles in Gravitation Theory Composite Spinor Bundles in Gravitation Theory

1995-02-08

arxiv.org/abs/gr-qc/9502022v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pp, LaTeX file

Scientific paper

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 $S\to\Si\to X$ where values of tetrad fields play the role of parameter coordinates, besides the familiar world coordinates.

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