Variations of the Speed of Light with Frequency and Implied Photon Mass

A general frequency-dependent dispersion relation of the speed of light in different mediums (vacuum, insulator, plasma) is deduced based on the Proca equations. Several recent astronomical observations of the pulsars are used to set the limits on the photon rest mass by this method and several upper bounds of larger than one order improvement than previous similar results are obtained. Considering the dispersion of the massive photon, the possible upper limits on the photon rest mass are also derived from the recently experimental results for testing the constancy of the speed of light in special relativity.