Abstract
The effective Lagrangian and mass operator are calculated for planar charged massive and massless fermions in a constant external homogeneous magnetic field in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED_{2+1}). We obtain the renormalizable effective Lagrangian and the fermion mass operator for a charged fermion of mass m and then calculate these quantities for the massless case. The radiative corrections to the mass of charged massless fermion when it occupies the lowest Landau level are found for the cases of the pure QED_{2+1} as well as the so-called reduced QED_{3+1} on a 2-brane. The fermion masses were found can be generated dynamically in an external magnetic field in the pure QED_{2+1} if the charged fermion has small bare mass m_0 and in the reduced QED_{3+1} on a 2-brane even at m_0=0. The dynamical mass seems to be likely to be revealed in monolayer graphene in the presence of constant homogeneous magnetic field (normal to the graphene sample).
Highlights
The radiative one-loop shift of an electron energy in the ground state in a constant homogeneous magnetic field in QED2+1 was calculated in [10] and the one-loop electron self-energy in the topologically massive QED2+1 at finite temperature and density was obtained in [11]
The effective Lagrangian, the electron mass operator and the density of vacuum electrons in an external constant homogeneous magnetic field were derived in the one-loop QED2+1 approximation in [12]
The polarization operator in graphene in a strong constant homogeneous magnetic field perpendicular to the graphene membrane has been obtained in the one-loop approximation of the QED2+1 in [9,13,14,15]
Summary
The radiative one-loop shift of an electron energy in the ground state in a constant homogeneous magnetic field in QED2+1 was calculated in [10] and the one-loop electron self-energy in the topologically massive QED2+1 at finite temperature and density was obtained in [11]. The effective Lagrangian, the electron mass operator and the density of vacuum electrons (induced by the background field) in an external constant homogeneous magnetic field were derived in the one-loop QED2+1 approximation in [12]. The one-loop self-energy of a Dirac electron of mass m in a thin medium simulating graphene in the presence of external magnetic field was investigated in the reduced QED3+1 on a 2brane in [19], in which it was shown that the radiative mass correction in the lowest Landau level does not vanish at the limit m → 0. We calculate the effective Lagrangian and the mass operator of planar charged fermions in the presence of an external constant homogeneous magnetic field in the one-loop approximation of the QED2+1. This formula coincides with the corresponding result obtained in [26,27]
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