Chiral kinetic theory with self-energy corrections and neutrino spin Hall effect

We systematically derive the chiral kinetic theory for chiral fermions with collisions, including the self-energy corrections, from quantum field theories. We find that the Wigner functions and chiral kinetic equations receive both the classical and quantum corrections from the self-energies and their spacetime gradients. We also apply this formalism to study nonequilibrium neutrino transport due to the interaction with thermalized electrons and nucleons, as realized in core-collapse supernovae. We derive neutrino currents along magnetic fields and neutrino spin Hall effect induced by the density gradient at first order in the Fermi constant $G_{\rm F}$ for anisotropic neutrino distributions.