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Polarization of vacuum by an external magnetic field in the (2+1)-dimensional quantum electrodynamics with a nonzero fermion density

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Abstract

The Green's function of the Dirac equation with an external stationary homogeneous magnetic field in the (2+1)-dimensional quantum electrodynamics (QED 2+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-loopQED 2+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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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. R. Khalilov

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  1. V. R. Khalilov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 132–151, October, 2000.

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Khalilov, V.R. Polarization of vacuum by an external magnetic field in the (2+1)-dimensional quantum electrodynamics with a nonzero fermion density. Theor Math Phys 125, 1413–1430 (2000). https://doi.org/10.1007/BF02551045

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