Reflections on Noether’s second theorem and the energy-momentum tensor

Freese, Adam

doi:10.1103/wmz3-lrbz

Reflections on Noether’s second theorem and the energy-momentum tensor

Journal Article · Fri Jan 09 00:00:00 EST 2026 · Physical Review. D.

DOI:https://doi.org/10.1103/wmz3-lrbz· OSTI ID:3012598

^[1]

Southeastern Universities Research Associations (SURA), Newport News, VA (United States). Center for Nuclear Femtography; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

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 the previous work, 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.

View Accepted Manuscript (DOE)

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 3012598

Report Number(s):: DOE/OR/23177--7875; JLAB-THY--25-4355; arXiv:2506.04510

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 113; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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