Some exact identities connecting one- and two-particle Green's functions in spin–orbit coupling systems

Some exact identities connecting one- and two-particle Green's functions in the presence of spin–orbit coupling have been derived. These identities are similar to the Ward identity in usual quantum transport theory of electrons. A satisfying approximate calculation of the spin transport in spin–orbit coupling system should also preserve these identities, just as the Ward identities should be remained in the usual electronic transport theory.