Remormalization group and ladder approximation in the field theory

The method partially exceeding the limits of the pertubation theory is suggested for the calculation of the Gell-Mann-Low (L)GM function and anomalous dimensions. The six-dimensional theory of the Λ PSI63 scalar/n a/ field with dimensionless coupling constant is used as an example. The two-point Green function and vertex function necessary for the GML function discovering are calculated in the ladder approximation. In the expressions for the mass operator and the vertex only the Feinman diagram sums are taken into account. The method of renormalization of mass operator in the ladder approximation coordinated with the usual renormalization theory in order to avoid divergences. With this aim in view the ladder approximation is presented as a result of suitable linearization of the Daison-Schwinger equations. The massless theory is considered to obtain evident solutions of these equations. It is found out that the GML function has an ultraviolet stable point in zero, it resulting from this that the theory is asymptotically free