Energy-momentum tensor from diffeomorphism invariance in classical electrodynamics
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914275222618112 |
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| author | Choi, Taeseung |
| author_facet | Choi, Taeseung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy-momentum tensor from diffeomorphism invariance in classical electrodynamics Choi, Taeseung High Energy Physics - Theory Mathematical Physics 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. |
| title | Energy-momentum tensor from diffeomorphism invariance in classical electrodynamics |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2601.16477 |