ANALYTICAL PROPERTIES OF THE QUADRATIC DENSITY RESPONSE AND QUADRATICDYNAMICAL STRUCTURE FUNCTIONS - CONSERVATION SUM-RULES AND FREQUENCY MOMENTS

The quadratic density response function and the quadratic dynamical st ructure function (the Fourier transform of the equilibrium three-point density correlations) contain important information about a many body system; they are also ingredients for an improved dynamical mean fiel d theory for strongly coupled Fermi systems. We examine the analytic p roperties of the density response function and establish new single fr equency and double frequency moment sum rules. We relate the sum rule coefficients to the high frequency expansion of the response function. Next we invoke the quadratic fluctuation-dissipation theorem to relat e these frequency moments to weighted frequency moments of the dynamic al structure function. These latter reduce to straight frequency momen ts in the high temperature classical and zero temperature degenerate l imits.