Infrared asymptotics of Green's functions and gauge invariant effective lagrangian in quantum chromodynamics

Problems connected with infrared asymptotic behaviour of Green functions in quantum chromodynamics with the help of Schwinger-Dyson equations are considered. In the framework of the assumptions made which seem to be reasonable in the infrared region there has been obtained that the massive solution of the Schwinger-Dyson equation for spinor propagator may be realized. In particular gauge this solution has a simple pole on the mass shell. For this solution to be realized the value of parameter γ which is the exponent of the infrared singularity of the full gluon propagator equals 2. The conclusion that the asymptotics of gluon propagator D(k) has the form 1/(k2)2 at k2 → 0 whereas the triple gluon vertex function has quite a definite form is to be the main result. These results enable to formulate unambiguously the gauge invariant Lagrangian effective in the infrared region at n=4 (n is momentum space dimension)