Relativistic hydrodynamics with spin

In this talk, I will present our development of a new framework
for relativistic perfect-fluid hydrodynamics that includes spin degrees of
freedom, building on recent theoretical advancements aimed at explaining
spin polarization in heavy-ion collisions. While standard relativistic
hydrodynamics has successfully described the properties of the
strongly-interacting matter produced in these collisions, understanding
the differential measurements of spin polarization remains a challenge.
Current models have partially explained experimental data by coupling spin
polarization with the vorticity of the medium. However, these models
suggest that spin should be treated as an independent degree of freedom,
whose dynamics are not solely tied to flow circulation. Assuming spin as a
macroscopic property, we propose that its dynamics should follow
hydrodynamic laws in equilibrium. Our framework is derived from quantum
kinetic theory for Dirac fermions and models the dynamics of matter in
relativistic heavy-ion collisions. Assuming small polarization effects, we
derive conservation laws for the net-baryon current, the energy-momentum
tensor, and the spin tensor based on de Groot–van Leeuwen–van Weert
definitions. We explore the properties of the spin polarization tensor,
analyze the propagation properties of its components, and derive the
spin-wave velocity for arbitrary statistics. Our findings indicate that
only transverse spin components propagate, similar to electromagnetic
waves. Furthermore, we investigate the spacetime evolution of spin
polarization in systems with certain symmetries and calculate the mean
spin polarization per particle, comparing our results with experimental
data. Our results show qualitative agreement with experimental
observations and other models for some observables. Additionally, we
examine the impact of external electric fields on spin polarization
dynamics within a Bjorken-expanding background.