Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density
arXiv:1712.02704 · doi:10.1142/S0217751X18500045
Abstract
Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. [1]-[3], the non-perturbative vacuum polarization effects in the 2+1 D supercritical Dirac-Coulomb system with are explored. Both the vacuum charge density and vacuum energy are considered. The main result of the work is that in the overcritical region turns out to be a rapidly decreasing function with and being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I we consider the evaluation and behavior of the vacuum density , which further is used in the part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for and behavior of the integral induced charge in the overcritical region.
25 pages, 13 figures
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