Angular Momentum and Energy-Momentum Densities as Gauge Currents

TL;DR

This paper presents a gauge theory perspective of general relativity by deriving angular momentum and energy-momentum densities as gauge currents from tangent space transformations, offering a novel interpretation of these quantities.

Contribution

It introduces a framework where angular momentum and energy-momentum tensors are derived as gauge currents from tangent space transformations, reinterpreting general relativity as a gauge theory.

Findings

Angular momentum and energy-momentum tensors are obtained as gauge currents.

Transformations in tangent space lead to a gauge theory formulation of gravity.

The approach offers a new perspective on conserved quantities in general relativity.

Abstract

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.