  Within the framework of the operator product expansion (OPE) and the
renormalization group equation (RGE), we show that the temperature and chemical
potential dependence of the zeroth moment of a spectral function (SF) is
completely determined by the one-loop structure of an asymptotically free
theory. This exact result constrains the shape of SF's, and implies a highly
non-trivial functional form for the SF near second order, or weak first order,
phase transitions. Phenomenological parameterizations of the SF, often used in
applications such as the analysis of lattice QCD data or QCD sum rule
calculations at finite temperature and baryon density, must satisfy these
constraints.
