Quantum theory of frequency shifts of an electromagnetic wave interacting with a plasma

In the paper we calculate the frequency shift induced on a photon by the interaction with a low density electronic plasma. The technique is the standard perturbation theory of quantum electrodynamics, taking into account the many body character of the plasma. The shift in non relativistic approximation is shown to be blue. Besides the quantum shift also the known classical effects and the correct temperature dependence are obtained. Finally the limits of the approximations used are discussed.