Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries

TL;DR

This paper generalizes a method for constructing invariant conserved currents and charges in gravity theories to include arbitrary local gauge symmetries, extending previous work from Lorentz to more general gauge groups.

Contribution

The paper introduces a unified approach to derive invariant conserved quantities in gravity theories with various local gauge symmetries, including non-Abelian and metric-affine gravity.

Findings

Applicable to Maxwell and Yang-Mills fields coupled to gravity

Extended to metric-affine gravity with local general linear group

Provides a systematic way to construct conserved currents in diverse gauge gravity theories

Abstract

Previously, we have developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now generalized to the case when the local Lorentz group is replaced by an arbitrary local gauge group. The particular examples include the Maxwell and Yang-Mills fields coupled to gravity with Abelian and non-Abelian local internal symmetries, and the metric-affine gravity in which the local Lorentz spacetime group is extended to the local general linear group.