Asymptotic solution of Schwinger -- Dyson equation for the gluon propagator in the infrared region

Abstract

The equation for the gluon propagator in the approach of Baker-Ball-Zachariasen is considered. The possibility of non-integer power infrared behaviour is studied, $D(q)\sim (q^2{)}^{-c}$, $q^2\to 0$. It is shown that the characteristic equation for the exponent has no solutions at $-1\le c\le 3$. The approximations made to obtain the closed integral equation are analysed and the conclusion on the infrared behaviour of the gluon propagator $D(q)\sim 1/(q^2{)}^2$, $q^2\to 0$ is made when the transverse part of the triple gluon vertex is taken into account.

11 pages, LATEX