A symmetry-based resolution of pseudo-gauge ambiguities in local equilibrium

Abstract

The total angular momentum current can be decomposed into orbital and spin contributions in different ways, known as pseudo-gauges. This freedom leads to ambiguities in the definition of local-equilibrium density operators, which in turn affect estimates of spin polarization in heavy-ion collisions. In this work, the pseudo-gauge ambiguity, together with other ambiguities associated with improvements of conserved currents, is reformulated in terms of spurious symmetries corresponding to conserved currents with vanishing total charge. A prescription for the unambiguous definition of a local-equilibrium density operator is introduced using the currents associated with genuine symmetries. The resulting density operator is invariant under transformations that add improvement terms to local currents, including the energy-momentum tensor.