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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.

It has been demonstrated that Statistical Hadronization Model fits perfectly to particle yields at freeze-out in heavy-ion and hadron collisions at LHC, RHIC and SPS, where quark-gluon plasma is created. It is however entirely not clear if particles emitted in the few-GeV energy regime can be understood as emerging from thermalized hadronic medium. Our recent work suggests that this might be the case. By implementing appropriate fireball geometry and expansion pattern in the THERMINATOR (THERMal heavy IoN generATOR) it was possible to describe not only yields, but also the spectra of most abundant particles measured at GSI SIS18. Most of the latter are pure prediction of the model. We present details of the model and extended comparison with experimental data and discuss further developments.

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 ωμν is introduced. It plays a role of a Lagrange multiplier conjugated to the spin tensor Sλ,μν. The space-time evolution of the spin polarization tensor depends on the specific form chosen for the spin tensor.