On Spinor Representations in the Weyl Gauge Theory

TL;DR

This paper introduces a novel 16-component spinor representation in Weyl non-Abelian gauge theory, constructed via external differential forms, and explores its gauge invariance and relation to torsion fields.

Contribution

It presents a new spinor representation in Weyl gauge theory using differential forms and establishes its gauge invariance and connection to Cartan torsion.

Findings

A 16-component spinor current-source is constructed.

The spinor representation is gauge-invariant.

Connections between gauge potential and torsion are analyzed.

Abstract

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it is a 16-component quantity for which a gauge-invariant Lagrangian is determined. The connexion between the Weyl non-Abelian gauge potential and the Cartan torsion field and the problem of a possible manifestation of the considered interactions are considered.