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

Finite temperature sum rules in the vector channel at finite momentum