Gaussian pseudogauge invariant hydrodynamics with spin

TL;DR

This paper develops a covariant fluctuating hydrodynamics framework with spin, incorporating torsion and ensuring pseudo-gauge invariance through gravitational Ward identities.

Contribution

It extends Gaussian covariant hydrodynamics to include torsion and spin, establishing pseudo-gauge invariance in the dynamics.

Findings

Formulated a pseudo-gauge invariant hydrodynamics with spin.

Derived second order gravitational Ward identities in torsionful spacetime.

Clarified the role of pseudo-gauge in hydrodynamics with spin.

Abstract

Extending the Gaussian covariant hydrodynamics approach [1] using torsion as an auxiliary field we formulate a fluctuating hydrodynamics with spin which is covariant with respect to pseudo-gauge transformations as well as generally covariant with respect to foliations. This is done via the second order gravitational Ward identities, derived here in the torsionful case. This ensures that, while angular momentum observables depend covariantly on the pseudo-gauge, the dynamics is pseudo-gauge independent, thus clarifying the role of the pseudo-gauge in hydrodynamics with spin