Analyticity in liquid metals

The analytic properties are examined for several multiple-scattering theories of liquid metals. A condition is obtained for a positive density of states in terms of the properties of the kernel of an integral equation obeyed by the self-energy path operator. It is found that this condition is obeyed by the Gyorffy-Korringa-Mills theory as well as the quasicrystalline approximation. The theories are reformulated in terms of relative coordinates and the implications of these results on the conductivity problem are discussed.