Improved Energy-Momentum Currents in Metric-Affine Spacetime

TL;DR

This paper extends the concept of energy-momentum currents from Minkowski spacetime to metric-affine spacetime, deriving improved conserved currents associated with scale and conformal symmetries without involving gravitational dynamics.

Contribution

It introduces a natural extension of energy-momentum currents to metric-affine spacetime, ensuring conservation laws for scale and conformal symmetries through affine Noether identities.

Findings

Conserved dilation and conformal currents are derived in metric-affine spacetime.

Conservation depends on the trace of the energy-momentum current satisfying a scaling relation.

No gravitational dynamics are involved in the current construction.

Abstract

In Minkowski spacetime it is well-known that the canonical energy-momentum current is involved in the construction of the globally conserved currents of energy-momentum and total angular momentum. For the construction of conserved currents corresponding to (approximate) scale and proper conformal symmetries, however, an improved energy-momentum current is needed. By extending the Minkowskian framework to a genuine metric-affine spacetime, we find that the affine Noether identities and the conformal Killing equations enforce this improvement in a rather natural way. So far, no gravitational dynamics is involved in our construction. The resulting dilation and proper conformal currents are conserved provided the trace of the energy-momentum current satisfies a (mild) scaling relation or even vanishes.