Methods for calculating multi-loop diagrams and renormalization group analysis of psi4-theory

Effective methods for evaluating renormalization group quantities are developed. The methods make it possible to compute the diagrams with all external momenta put equal to zero. The Gell-Mann-Low function of phi4-theory is calculated in the three-and four-loop approximations using different renormalization schemes. The dependence of this function on the ratios of external momenta is studied