Relativistic hydrodynamics with spin

TL;DR

This paper reviews a new framework for perfect-fluid relativistic hydrodynamics that includes spin 1/2 particles, deriving equations from conservation laws and introducing a spin polarization tensor as a key component.

Contribution

It presents a novel approach to relativistic hydrodynamics incorporating spin degrees of freedom through a spin polarization tensor derived from conservation laws.

Findings

Hydrodynamic equations follow from energy, momentum, and angular momentum conservation.

The spin polarization tensor acts as a Lagrange multiplier in the framework.

The evolution of the spin polarization tensor depends on the chosen form of the spin tensor.

Abstract

A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The incorporation of the angular-momentum conservation requires that the spin polarization tensor is introduced. It plays a role of a Lagrange multiplier conjugated to the spin tensor. The space-time evolution of the spin polarization tensor depends on the specific form chosen for the spin tensor.