Sketch of a gauge model of gravity with SU(2) symmetry on a Lorentzian manifold with tetrad

TL;DR

This paper proposes a gauge model of gravity with SU(2) symmetry on a Lorentzian manifold, interpreting the Yang-Mills field as the gravitational interaction for fundamental fermions, derived from Dirac-Yang-Mills equations.

Contribution

It introduces a novel SU(2) gauge model of gravity on a Lorentzian manifold using a tetrad, linking Yang-Mills fields to gravitational interactions for fermions.

Findings

Derivation of Dirac-Lanczos-Yang-Mills equations with SU(2) symmetry

Interpretation of Yang-Mills field as gravitational interaction

Extension of Standard Model equations to include gravity

Abstract

A gauge model with SU(2) symmetry is proposed to describe the gravitational interaction of fundamental fermions (leptons and quarks) on a Lorentzian manifold with a tetrad. From the system of Dirac-Yang-Mills equations underlying the Standard Model, we arrive at a model system of Dirac-Lanczos-Yang-Mills equations, written using second-order matrices. This system of equations has an additional gauge symmetry with respect to the unitary group SU(2). The Yang-Mills field associated with this gauge group is interpreted as the gravitational field interacting with fundamental fermions.