One-loop diagrams in quantum gravity coupled to scalar electrodynamics

In nonsupersymmetric-covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. There were two kinds of methods to reach this result: diagrammatic calculation and heat kernel expansion. On the other hand, more symmetry requirements make the theory finite and it was analyzed how it is possible. In this paper, based on diagrammatic calculation, we consider Einstein–Scalar electrodynamics (Einstein–SQED) system which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. Although it is known that fermionic loop can cancel the divergent terms as in the case of supersymmetric theory, there might be accidental cancellation by the equation of motion at a low probability. It is worth to study because there is no such attempt for this model yet and it can be checked easily using the existing result. We introduce how to calculate the possible one-loop diagrams in Einstein–SQED system and show how divergent terms are not vanished with the results calculated earlier.

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Nonperturbative vacuum polarization effects are explored for a supercritical Dirac–Coulomb system with [Formula: see text] in 2+1[Formula: see text]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 [Formula: see text] and vacuum energy [Formula: see text] 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 I4 for [Formula: see text], in the present part II, the evaluation of the vacuum energy [Formula: see text] is investigated with emphasis on the renormalization and convergence of the partial expansion for [Formula: see text]. 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 nonperturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters 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. To the end the similarity in calculations of [Formula: see text] in 2+1 and 3+1[Formula: see text]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 [Formula: see text] in 3+1[Formula: see text]D.