Finite temperature sum rules in the vector channel at finite momentum

Exact sum rules for the longitudinal and transverse part of the vector channel spectral functions at non-zero 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.