Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. II. Vacuum energy

Abstract

Non-perturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with $Z>Z_{cr,1}$ in 2+1 D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. [1]-[3]. Both the vacuum charge density ${\rho }_{VP}(\vec{r})$ and vacuum energy ${\mathcal{E}}_{VP}$ are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I [4] for ${\rho }_{VP}$, in the present part II the evaluation of the vacuum energy ${\mathcal{E}}_{VP}$ is investigated with emphasis on the renormalization and convergence of the partial expansion for ${\mathcal{E}}_{VP}$. It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially non-perturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region ${\mathcal{E}}_{VP}$ turns out to be a rapidly decreasing function $\sim -{\eta }_{eff}{Z}^3/R$ with ${\eta }_{eff}>0$ and $R$ being the size of the external Coulomb source. To the end the similarity in calculations of ${\mathcal{E}}_{VP}$ in 2+1 and 3+1 D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for $Z\gg Z_{cr,1}$ in 3+1 D.

20 pages, 29 figures

References in corpus (11)

• Quantum transport of massless Dirac fermions in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Nonlinear screening of charge impurities in graphene
• Supercritical Coulomb Impurities in Gapped Graphene
• Polarization Charge Distribution in Gapped Graphene
• Electric field of a pointlike charge in a strong magnetic field and ground state of a hydrogenlike atom
• Positronium collapse and the maximum magnetic field in pure QED
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
• Bethe-Salpeter approach for relativistic positronium in a strong magnetic field
• Vacuum energy of one-dimensional supercritical Dirac-Coulomb system
• Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density

Cited by in corpus (1)

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