Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density

@article{Davydov2017NonperturbativeVP,
  title={Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density},
  author={Andrey Davydov and K. Sveshnikov and Yulia E. Voronina},
  journal={arXiv: High Energy Physics - Theory},
  year={2017}
}
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… 
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