The kinetic equation for the quark Wigner function in strong gluon field

The Vlasov type quantum kinetic equation for deconfined quarks in strong quasi-classical gluon field is derived in the covariant single-time formalism. The equations system for the Wigner function components is obtained as a result of spinor and color decomposition. The field-free and vacuum solutions of the kinetic equation are found, and the conservation laws are derived. The flux-tube configuration of gluon field is discussed in detail.