Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

The polarization operator (tensor) for planar charged fermions in a constant uniform magnetic field is calculated in the one-loop approximation of 2+1 -dimensional quantum electrodynamics (QED 2+1 ) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in QED 2+1 at a finite chemical potential, find the imaginary part of this Green function, and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem likely to be revealed in a monolayer graphene sample in the presence of an external constant uniform magnetic field B perpendicular to it