Radiation of a point charge uniformly moving in a dielectric medium

We analyse how the frequency dependence of the dielectric permittivity affects the electromagnetic field radiated by a point charge uniformly moving in a medium. It turns out that a moving charge radiates at every velocity. We study the space distribution of the electromagnetic field and show that its oscillations are due to the time-dependent polarization of the medium induced by the moving charge. Spectral distributions of the radiated energy and the photon number are given. Consequences arising from a choice of polarization different from the usual one are discussed. An analysis of the Kramers-Kronig dispersion relations for the treated problem is given. This consideration may be useful for the experiments recently discussed in the literature.