Constraints on the photon production calculated by kinetic approaches are studied by means of sum rules at finite temperature for simple quantum systems. For the square-well potential the exact production rate is compared with its semi-classical limit in order to introduce the principle problem. For the scattering of hard spheres the photon-production cross section is derived exactly by a partial-wave expansion. This serves to study the more realistic example of a gas of hard spheres. The corresponding kinetic-photon production rates are found to violate the sum rules, due to a singular behaviour at small gamma energies. Thus the hypothesis of incoherent free scattering is not valid in that range because of destructive interferences which quench the production rates significantly. For the application to nuclear collisions at intermediate energies these quenching effects are found to be important for gamma energies even up to a few hundred MeV.