Abstract
Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. 1–3, the nonperturbative vacuum polarization effects in the 2+1[Formula: see text]D supercritical Dirac–Coulomb system with [Formula: see text] are explored. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. The main result of the work is that in the overcritical region [Formula: see text] turns out to be a rapidly decreasing function [Formula: see text] with [Formula: see text] and [Formula: see text] 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 [Formula: see text], which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for [Formula: see text] and behavior of the integral induced charge [Formula: see text] in the overcritical region.
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