Plane density of induced vacuum charge in a supercritical Coulomb potential

TL;DR

This paper derives and analyzes the induced vacuum charge density in a strong Coulomb potential, revealing differences between massive and massless fermions, with potential applications to graphene systems.

Contribution

It provides a new expression for the planar induced vacuum charge density using a self-adjoint extension approach, applicable to both subcritical and supercritical regimes.

Findings

Vacuum charge density exhibits screening behavior.

Differences in charge density between massive and massless fermions.

Potential experimental testing in graphene with supercritical impurities.

Abstract

An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. We calculate the real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in the supercritical Coulomb potential due to the so-called real vacuum polarization. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.