The Energy-Momentum Tensor(s) in Classical Gauge Theories

TL;DR

This paper reviews the construction and properties of energy-momentum tensors in classical gauge theories, introducing a new gauge-invariant, symmetric tensor for non-Abelian gauge fields and matter, and discussing their relation to gravity.

Contribution

It presents a novel, simple gauge invariance-based method for improving the energy-momentum tensor in non-Abelian gauge theories, ensuring gauge invariance and symmetry.

Findings

Introduces a new gauge-invariant, symmetric energy-momentum tensor

Clarifies the relationship with the Einstein-Hilbert tensor

Provides a comprehensive review of energy-momentum tensors in gauge theories

Abstract

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.