The problem of photon propagation in a medium in presence of a strong magnetic field in the frame of quantum electrodynamics is discussed in the present paper, based on previous literature in this area. The breaking of the spatial symmetry by the magnetic field determine the existence of a set of basic vectors and tensors which must satisfy the gauge and CPT invariance of quantum electrodynamics. The charge symmetric and non-symmetric cases are discussed. In the second case the Faraday effect is produced. A chiral current arises, associated to a pseudovector eigenvector ofthe polarization operator (due to the breaking of the spatial symmetry by the external magnetic field), related to the so-called axial anomaly. The path integrals and functional derivation are widely used to obtain the self-energy and vertex operators, and the Dyson equations. The inadequate introduction of a chiral chemical potential in the standard model is discussed for the Weinberg-Salam model for electroweak interactions.
Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field
