Relativistic spin hydrodynamics with antisymmetric spin tensors and an extension of the Bargmann-Michel-Telegdi equation

TL;DR

This paper develops a relativistic spin hydrodynamics framework with antisymmetric spin tensors, extending the Bargmann-Michel-Telegdi equation to include new spin-hydrodynamic couplings and thermodynamic consistency.

Contribution

It introduces a novel formulation of relativistic spin hydrodynamics with antisymmetric spin tensors satisfying the Frenkel-Mathisson-Pirani condition, extending the BMT equation with additional coupling terms.

Findings

Thermodynamics is consistent with spin-induced corrections.

The model reproduces inverse spin Hall and anomalous Hall effects in the nonrelativistic limit.

Extended BMT equation includes Thomas precession, spin-rotation, and new couplings.

Abstract

We derive a formulation of relativistic spin hydrodynamics with totally antisymmetric spin tensors that satisfy the Frenkel-Mathisson-Pirani condition. In our proposed spin hydrodynamics, the second law of thermodynamics is fulfilled by the spin-induced corrections in the heat flow, the viscous tensor, and the antisymmetric part of the energy-momentum tensor. These corrections are interpreted as the inverse spin Hall effect and the anomalous Hall effect in the nonrelativistic limit. We show that our evolution equation for the spin density is interpreted as an extension of the Bargmann-Michel-Telegdi equation known in relativistic many-body systems, including the Thomas precession term, the spin-rotation term, and new coupling terms between spin and hydrodynamic variables.