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The rotation of the polarization vector for light propagating perpendicularto an external constant external magnetic field $B$, is calculated in quantumvacuum, where it leads to different photon eigenmodes of the magnetized photonself-energy tensor for polarizations along and orthogonal to $B$ (Cotton-Moutoneffect in QED vacuum). Its analogies and differences with Faraday effect arediscussed and both phenomena are calculated for a relativistic electron gas atlow densities, by starting from the low energy limit of the photon self-energyeigenvalues in presence of $B$. In the Cotton-Mouton case the polarizationvector describes an ellipse whose axes vary periodically from zero to a maximumvalue. By assuming an effective electron density of order $10^3$ cm$^{-3}$ thequantum relativistic eigenvalues lead to a rotation of the polarization planecompatible with some of the limit values reported by PVLAS experiments. Otherconsequences, which are interesting for astrophysics, are also discussed.

Polarization rotation for light propagating non-parallel to a magnetic field in QED vacuum and in a dilute electron gas