Quantum transport theory with vector interaction

Abstract: We derive the relativistic quantum kinetic equation for massless fermions with vector and axial vector interaction using the Wigner function formalism. The vector and axial vector currents are self-consistently treated with corresponding constraint equations. The kinetic equations are derived and the condition for equilibrium is discussed up to the first order of $\hbar$. In addition to the vorticity and shear contributions, the divergence of the local particle number density is also found to contribute to the kinetic equations.