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Title: 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 trans-lations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translationsrather than constant ones, a unique, symmetric, and gage-invariant energy-momentum tensor emerges that satisfies a genuineoff-shell Noether identity without invoking the equations of motion. For the free electromagnetic field, this tensor coincideswith the familiar Belinfante-Rosenfeld and Bessel-Hagen expressions, but arises here directly from spacetime-dependenttranslation symmetry rather than from improvement procedures or compensating gage transformations. In interacting clas-sical electrodynamics, comprising a point charge coupled to the electromagnetic field, diffeomorphism invariance yieldswell-defined energy-momentum tensors for the field and the particle, while the interaction term itself generates no inde-pendent local energy-momentum tensor. Its role is instead entirely encoded in the coupled equations of motion governingenergy-momentum exchange, thereby resolving ambiguities in the local definition of the energy-momentum tensor presentin canonical and improvement-based approaches.

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