WARD IDENTITIES FOR INTERACTING ELECTRONIC SYSTEMS

A Ward-Takahashi identity, as a consequence of gauge invariance and in a form that relates self-energy to the two-particle Bethe-Salpeter sc attering kernel, was first derived by Vollhardt and Wolfle for a syste m of independent particles moving in a random medium. This is generali zed to a class of interacting electronic systems in materials with or without random impurities, following a procedure previously used for c lassical wave transport in disordered media. This class of systems als o possesses other symmetry properties such as invariance under time tr anslations and local spin rotations, which imply local conservation la ws for energy and spin current. They imply additional Vollhardt-Wolfle type identities. We present non-perturbative derivations of these ide ntities, and consider the constraints they impose on the relationship between the self-energy and the two-particle scattering kernel. (C) 19 98 Published by Elsevier Science B.V.