Radiative effects in two-dimensional models of quantum electrodynamics in a constant magnetic field

Abstract

The radiative energy shift of an electron in a constant magnetic field has been considered in the framework of the ($2+1$)-dimensional quantum electrodynamics with four-component fermions as well as in reduced ${\mathrm{QED}}_{3+1}$ in which photons propagate in a ($3+1$)-dimensional bulk and fermions are localized on a 2-brane. Analytical expressions are obtained for the energy of interaction of the electron spin with an external field and the radiative shift of the electron mass after averaging over the spin states of the electron. For ultrarelativistic energies of an electron and relatively weak magnetic fields, the total probability of a photon emission by a massive electron and the anomalous magnetic moment of an electron in a reduced ${\mathrm{QED}}_{3+1}$ are calculated. The dependence of the obtained values on the invariant dynamic parameter of synchrotron radiation is investigated. The total probabilities of synchrotron radiation of a charged massless fermion and the production of a pair of charged massless fermions by a photon in an external magnetic field are calculated in ($2+1$)-dimensional models of quantum electrodynamics.