Spin tensor and its role in non-equilibrium thermodynamics

TL;DR

This paper explores how the choice of stress-energy tensor affects the description of relativistic fluids, emphasizing the importance of including a spin tensor for accurate modeling of polarized fluids in non-equilibrium thermodynamics.

Contribution

It introduces the necessity of a spin tensor in relativistic hydrodynamics to accurately describe polarized fluids and highlights differences in predictions based on tensor choice.

Findings

Different stress-energy tensors lead to distinct predictions for particle polarization.

The Belinfante tensor is inadequate for fluids with slow polarization relaxation.

Including a spin tensor extends relativistic hydrodynamics to better model polarized fluids.

Abstract

It is shown that the description of a relativistic fluid at local thermodynamic equilibrium depends on the particular quantum stress-energy tensor operator chosen, e.g., the canonical or symmetrized Belinfante stress-energy tensor. We argue that the Belinfante tensor is not appropriate to describe a relativistic fluid whose macroscopic polarization relaxes slowly to thermodynamic equilibrium and that a spin tensor, like the canonical spin tensor, is required. As a consequence, the description of a polarized relativistic fluid involves an extension of relativistic hydrodynamics including a new antisymmetric rank-two tensor as a dynamical field. We show that the canonical and Belinfante tensors lead to different predictions for measurable quantities such as spectrum and polarization of particles produced in relativistic heavy-ion collisions.