Energy-momentum tensors in gauge theory

TL;DR

This paper explores the properties of energy-momentum tensors in gauge theories, highlighting their non-uniqueness, the persistence of the Noether component, and the impact of gauge invariance on conservation laws.

Contribution

It provides a detailed analysis of the structure and properties of energy-momentum tensors within gauge theories, emphasizing their non-uniqueness and the consequences of gauge invariance.

Findings

Multiple energy-momentum currents exist for a given gauge theory.

The Noether component of the energy-momentum current cannot be eliminated.

Energy-momentum conservation fails if the Lagrangian is not gauge-invariant.

Abstract

In field theory on a fibre bundle Y->X, an energy-momentum current is associated to a lift onto Y of a vector field on X. Such a lift by no means is unique, and contains a vertical part. It follows that: (i) there are a set of different energy-momentum currents, (ii) the Noether part of an energy-momentum current can not be taken away, (iii) if a Lagrangian is not gauge-invariant, the energy-momentum fails to be conserved.