Energy-momentum tensor from diffeomorphism invariance in classical electrodynamics
Abstract
We reexamine the energy-momentum tensor in classical electrodynamics from the perspective of spacetime-dependent translations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translations rather than constant ones, a unique, symmetric, and gauge-invariant energy-momentum tensor emerges that satisfies a genuine off shell Noether identity without invoking the equations of motion. For the free electromagnetic field, this tensor coincides with the familiar Belinfante-Rosenfeld and Bessel-Hagen expressions, but arises here directly from spacetime-dependent translation symmetry rather than from improvement procedures or compensating gauge transformations. In interacting classical electrodynamics, comprising a point charge coupled to the electromagnetic field, diffeomorphism invariance yields well-defined energy-momentum tensors for the field and the particle, while the interaction term itself generates no independent local energy-momentum tensor. Its role is instead entirely encoded in the coupled equations of motion governing energy-momentum exchange, thereby resolving ambiguities in energy-momentum localization present in canonical and improvement-based approaches.
Cite
@article{arxiv.2601.16477,
title = {Energy-momentum tensor from diffeomorphism invariance in classical electrodynamics},
author = {Taeseung Choi},
journal= {arXiv preprint arXiv:2601.16477},
year = {2026}
}