Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\mathcal{O}(\hslash )$, which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the $H$ function obeying Boltzmann’s $H$ theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing the chiral vortical effect.

• Received 20 March 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.021601