Abstract
The Green's function of the Dirac equation with an external stationary homogeneous magnetic field in the (2+1)-dimensional quantum electrodynamics (QED2+1) with a nonzero fermion density is constructed. An expression for the polarization operator in an external stationary homogenous magnetic field with a nonzero chemical potential is derived in the one-loopQED2+1 approximation. The contribution of the induced Chern—Simons term to the polarization operator and the effective Lagrangian for the fermion density corresponding to the occupation of n relativistic Landau levels in an external magnetic field are calculated. An expression of the induced Chern—Simons term in a magnetic field for the case of a finite temperature and a nonzero chemical potential is obtained.
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