Vacuum energy of one-dimensional supercritical Dirac-Coulomb system

Abstract: Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with $Z>Z_{cr}$ in 1+1 D. Both the vacuum charge density $\rho_{vac}(x)$ and vacuum energy $E_{vac}$ are considered. It is shown that in the overcritical region the behavior of vacuum energy could be significantly different from perturbative quadratic growth up to decrease reaching large negative values.