Understanding spin polarization using the Wigner function

Recent results on spin polarization in heavy ion collisions 
have challenged many of the preconceptions held by the community on the 
hydrodynamical treatment of the quark gluon plasma. Given such 
circumstances, it is imperative to develop a hydrodynamical framework 
that incorporates spin as a separate degree of freedom. In this talk, I 
will present our recent work on constructing 'spin' hydrodynamics by 
studying a weakly interacting massive fermionic gas in equilibrium using 
a quantum framework that utilizes the Wigner function. Furthermore, I 
will show how such a framework may be extended to massive vector 
particles and what can be done to address the case of Fermi-Dirac and 
Bose-Einstein statistics in spin-1/2 and spin-1 cases respectively.  Our 
analysis reveals a general structure of the hydrodynamical currents that 
may be modified to include viscous effects thus enabling us to make 
predictions on spin observables.