INDUCED VACUUM CHARGE OF MASSLESS FERMIONS IN COULOMB AND AHARONOV–BOHM POTENTIALS IN 2+1 DIMENSIONSстатья
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Дата последнего поиска статьи во внешних источниках: 24 октября 2016 г.
Аннотация:We study the vacuum polarization of zero-mass charged fermions in Coulomb and Aharonov–Bohm potentials
in 2+1 dimensions. For this, we construct the Green’s function of the two-dimensional Dirac equation
in the considered field configuration and use it to find the density of the induced vacuum charge in so-called
subcritical and supercritical regions. The Green’s function is represented in regular and singular (in the
source) solutions of the Dirac radial equation for a charged fermion in Coulomb and Aharonov–Bohm potentials
in 2+1 dimensions and satisfies self-adjoint boundary conditions at the source. In the supercritical
region, the Green’s function has a discontinuity related to the presence of singularities on the nonphysical
sheet of the complex plane of “energy,” which are caused by the appearance of an infinite number of
quasistationary states with negative energies. Ultimately, this situation represents the neutral vacuum
instability. On the boundary of the supercritical region, the induced vacuum charge is independent of
the self-adjoint extension. We hope that the obtained results will contribute to a better understanding of
important problems in quantum electrodynamics and will also be applicable to the problem of screening
the Coulomb impurity due to vacuum polarization in graphene with the effects associated with taking the
electron spin into account.