Essentially nonperturbative vacuum-polarization effects in a two-dimensional Dirac-Coulomb system for Z > Zcr: vacuum polarization effectsстатья

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Дата последнего поиска статьи во внешних источниках: 29 мая 2019 г.

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[1] Essentially nonperturbative vacuum-polarization effects in a two-dimensional dirac-coulomb system for z > zcr: vacuum polarization effects / K. A. Sveshnikov, Y. S. Voronina, A. S. Davydov, P. A. Grashin // Theoretical and Mathematical Physics. — 2019. — Vol. 199, no. 1. — P. 534–562. For a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge Z>Z_{cr,1} and radius R_0, we consider essentially nonperturbative vacuum-polarization effects in the overcritical region. Using results obtained in our preceding paper for the induced charge density ρ_{VP}({r}), we thoroughly consider the calculation of the vacuum energy E_{VP} based on the renormalization, the convergence of the partial expansion for ρ_{VP}({r}), and the behavior of the integral induced charge Q_{VP} in the overcritical region. In particular, we show that the renormalization using the fermionic loop with two external legs turns out to be a universal technique, which eliminates the divergence of the theory in the purely perturbative and essentially nonperturbative modes for ρ_{VP}({r}) and E_{VP}. The most significant result is that for Z ≥Z_{cr,1} in such a system, the vacuum energy becomes a rapidly decreasing function of the source charge Z reaching large negative values; its behavior is estimated from below (in absolute value) as ∼ −|η_{eff} Z^3|/R_0. We also study the dependence of the effect of the decrease in E_{VP} on the cutoff of the Coulomb asymptotics of the external field at different scales R_1 > R_0 and R_1 >> R_0. [ DOI ]

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