Reflections on Noether's second theorem and the energy-momentum tensor
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917167199420416 |
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| author | Freese, Adam |
| author_facet | Freese, Adam |
| contents | Through symmetry of the action under global spacetime translations, Noether's first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)], I had obtained a symmetric and gauge-invariant EMT by using Noether's second theorem instead, with local spacetime translations as the symmetry group. However, the derivation therein was flawed, containing a faulty assumption about the transformation rule for spinor fields. In this work, I revisit the derivation of [Phys. Rev. D 106, 125012 (2022)], both correcting the faulty step and simplifying the derivation for broader accessibility. The end result is an EMT for quantum chromodynamics that is gauge-invariant, but not symmetric. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflections on Noether's second theorem and the energy-momentum tensor Freese, Adam High Energy Physics - Phenomenology General Relativity and Quantum Cosmology Nuclear Theory Through symmetry of the action under global spacetime translations, Noether's first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)], I had obtained a symmetric and gauge-invariant EMT by using Noether's second theorem instead, with local spacetime translations as the symmetry group. However, the derivation therein was flawed, containing a faulty assumption about the transformation rule for spinor fields. In this work, I revisit the derivation of [Phys. Rev. D 106, 125012 (2022)], both correcting the faulty step and simplifying the derivation for broader accessibility. The end result is an EMT for quantum chromodynamics that is gauge-invariant, but not symmetric. |
| title | Reflections on Noether's second theorem and the energy-momentum tensor |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology Nuclear Theory |
| url | https://arxiv.org/abs/2506.04510 |