  Exact sum rules for the longitudinal and transverse part of the vector
channel spectral functions at nonzero momentum are derived in the first part of
the paper. The sum rules are formulated for the finite temperature spectral
functions, from which the vacuum component has been subtracted, and represent a
generalization of previous work in which sum rules were derived only for the
zero-momentum limit. In the second part of the paper, we demonstrate how the
sum rules can be used as constraints in spectral fits to lattice data at
various temperatures, with the latest dynamical lattice QCD data at zero
momentum.
