Fermions in Gravitation Theory

TL;DR

This paper discusses the representation of fermion fields in gravitation theory using composite spinor bundles, emphasizing the pairing with tetrad gravitational fields and their role as parameter coordinates.

Contribution

It introduces a novel geometric framework for fermions in gravitation theory using composite spinor bundles and tetrad fields.

Findings

Fermion fields are paired with tetrad gravitational fields.

Fermion-tetrad pairs are represented by sections of a composite spinor bundle.

Gravitational fields serve as parameter coordinates in this framework.

Abstract

In gravitation theory, a fermion field must be regarded only in a pair with a certain tetrad gravitational field. These pairs can be represented by sections of the composite spinor bundle $S\to\Si\to X^4$ where values of gravitational fields play the role of parameter coordinates, besides the familiar world coordinates.