Perfect spin hydrodynamics at all orders in spin polarization

We compare two recently developed frameworks of perfect spin hydrodynamics for spin-$1/2$ particles, based respectively on classical kinetic theory and the Wigner function. We show that the conserved currents in both approaches have the same form at each order of the expansion in the components of the spin polarization tensor $ω$. The only difference is a relative multiplicative factor, which is equal to 1 at the lowest nontrivial order and increases monotonically with the expansion order.

💡 Research Summary

The paper undertakes a systematic comparison of two recently formulated frameworks for perfect spin hydrodynamics of spin‑½ particles: a classical kinetic‑theory based approach and a quantum approach built on the Wigner function. Both frameworks aim to describe the same physical system—relativistic fluids with non‑vanishing spin polarization—yet they originate from fundamentally different theoretical premises. The classical description extends the phase‑space to include a spin four‑vector s^μ, following the Mathisson‑Papapetrou‑Dixon construction, and employs a Boltzmann‑type equilibrium distribution f_eq = exp