Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD

TL;DR

This paper resolves the ambiguity in defining the spin tensor in relativistic spin hydrodynamics by demonstrating that, in a specific interacting field theory model, the mean-field limit yields a canonical spin tensor consistent with non-dissipative spin hydrodynamics.

Contribution

It proves that the mean-field limit of a modified Nambu-Jona-Lasinio model with spin interactions produces a canonical spin tensor, clarifying the pseudogauge ambiguity.

Findings

Mean-field limit of the model aligns with non-dissipative spin hydrodynamics.

The pseudogauge ambiguity in the spin tensor can be resolved in interacting theories.

Canonical spin tensor emerges naturally in the mean-field approximation.

Abstract

The spin tensor is fundamental to relativistic spin hydrodynamics, but its definition is ambiguous due to the pseudogauge symmetry. We show that this ambiguity can be solved in interacting field theories. We prove that the mean-field limit of a modified Nambu-Jona-Lasinio model with spin-spin interactions is equivalent to nondissipative spin hydrodynamics with a canonical spin tensor.