Canonical currents without improvements: the QCD example

Tomi Koivisto

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arXiv · 2610.24040

Canonical currents without improvements: the QCD example

Tomi Koivisto

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Abstract

In conventional formulations of relativistic field theory, energy-momentum and angular-momentum currents are defined only up to improvement terms in flat spacetime, and in curved spacetime they are conserved only along symmetries of the metric. When defined as canonical Noether currents relative to an independent parallel frame, as in General Parallel Relativity, they are both unambiguous and conserved. For QCD, the gauge-invariant tensor, the Belinfante-Rosenfeld relation and the spin surface term follow from the variational principle. An exact coupled solution is shown to have conserved energy and rotation charges without the corresponding symmetries. Quarks of opposite helicity are indistinguishable by the metric and the symmetric energy-momentum tensor, yet carry opposite rotation charges.

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Tomi Koivisto. 2026-10-16. Canonical currents without improvements: the QCD example. https://arxiv.org/abs/2610.24040

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