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This will be a review of the state of the art in Spin hydrodynamics.
Abstract: Collective motion of spin degrees of freedom has been playing an increasingly prominent role both in high energy and condensed matter physics, especially after the observation of global polarization of Lambda hyperons in heavy ion collisions and generation of spin currents in liquid metals. In this talk, I will introduce a first principles construction of spin hydrodynamics, that is, relativistic hydrodynamics of spin currents coupled to stress tensor. The basic idea is to borrow the notion of ‘torsion' from General Relativity to remove the Belinfante-Rosenfeld ambiguities in definition of the spin currents, and use 'spin-connection', again a notion from the Einstein-Cartan theory, to introduce spin chemical potentials as dynamical variables for the hydrodynamical equation. We then apply this formulation to heavy ion collisions and find good agreement with data.