The non-perturbative approach to the infrared problem in QCD at finite temperature

A non-perturbative approach is developed for investigation of the infrared problem in QCD at T not= 0 in the ghost-free axial gauge. The problem is solved by using a 3-dimensional theory within the exact Slavnov-Taylor identities and Schwinger-Dyson equations. The system of two non-linear integral equations for the structural functions of the gluon polarization tensor is obtained whose solution determines the infrared behavior of the temperature Green functions in the 4-dimensional QCD. The simplest solution of these equations which is the same as the first term of the perturbation expansion shows the presence of singularities in the gluon propagator at momenta p approximately g2T, that cannot be eliminated by any choice of the gauge. The infrared instability of QCD at T not= 0 caused by these singularities is discussed. (author)