Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential.

We consider nonperturbative vacuum polarization effects in the supercritical region for a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge and radius in the magnetic field with an axial-vector potential. We study the behavior of the vacuum charge and vacuum current densities, and . We focus on the divergence in the theory corresponding to the renormalization and convergence of partial series for and . We stress that in contrast to the vacuum charge density, the partial channels with large values of the third projection of the total angular momentum must be taken into account in calculating the vacuum current density in the presence of an external magnetic field localized in the range . We show that in the presence of a supercritical Coulomb source, the induced magnetic field can enhance the original magnetic field for certain values of parameters of the external vector potential. [ABSTRACT FROM AUTHOR]