Conserved Currents for the Gauge-Field Theory with Lorentz Symmetry Group

TL;DR

This paper derives explicit conserved currents in a Yang-Mills gauge theory with Lorentz symmetry, linking them to the energy-momentum tensor and tetrad variables, and explores their implications for gravity and static fields.

Contribution

It introduces a novel explicit expression for conserved currents in Lorentz-symmetric gauge theories based on tetrad decomposition and energy-momentum tensor properties.

Findings

Conserved currents exist when the energy-momentum and Ricci tensors commute.

The currents enable a composite gravity theory.

Analysis of static isotropic fields around a point mass.

Abstract

For the Yang-Mills-type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.