Noether's theorems and the energy-momentum tensor in quantum gauge theories

TL;DR

This paper derives a symmetric, invariant energy-momentum tensor for quantum electrodynamics and quantum chromodynamics directly from Noether's second theorem, avoiding ad hoc improvements and ensuring consistency with quantum gauge symmetries.

Contribution

It provides a novel derivation of the energy-momentum tensor in quantum gauge theories using Noether's second theorem, ensuring symmetry and invariance inherently.

Findings

Derived EMT for QED and QCD from second theorem

EMT is automatically symmetric and invariant

No need for ad hoc improvement procedures

Abstract

Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while the second theorem identifies it as a conserved current associated with local spacetime translations. This work obtains an EMT for quantum electrodynamics and quantum chromodynamics through the second theorem, which is automatically symmetric in its indices and invariant under the expected symmetries (e.g., BRST invariance) without the need for introducing an ad hoc improvement procedure.