Equilibrium Spin Distribution From Detailed Balance

Abstract As the core ingredient for spin polarization, the equilibrium spin distribution function that eliminates the collision terms is derived from the detailed balance principle. The kinetic theory for interacting fermionic systems is applied to the Nambu–Jona-Lasinio model at quark level. Under the semi-classical expansion with respect to $$\hbar $$ ħ , the kinetic equations for the vector and axial-vector distribution functions are obtained with collision terms. For an initially unpolarized system, spin polarization can be generated at the first order of $$\hbar $$ ħ from the coupling between the vector and axial-vector charges. Different from the classical transport theory, the collision terms in a quantum theory vanish only in global equilibrium with Killing condition.