Orthogonality Catastrophe for a System of Interacting Electrons

The Anderson orthogonality theorem is derived for a general non · separable local potential. It is shown that the overlap integral is given for this general case by exp [- 2(2~i) ' Tr(!nS(It»'log N], where S(It) is the scattering S·matrix at the Fermi energy. This form of the overlap integral is also shown to hold for interacting conduction electrons if local potential V in the final state is replaced by the self · energy difference;E*(It) due to the local potential