Self-consistent renormalization as an efficient realization of main ideas of the Bogoliubov-Parasiuk R-operation

Abstract: By self-consistent renormalization (SCR) it is meant that all formal relations between UV-divergent Feynman amplitudes are automatically retained as well as between their regular values obtained in the framework of the SCR. The SCR is efficiently applicable on equal grounds both to renormalizable and nonrenormalizable theories. SCR furnishes new means for the constructive treatment of new subjects: i) UV-divergence problems associated with symmetries, Ward identities, and quantum anomalies; ii) new relations between finite bare and finite physical parameters of quantum field theories. The aim of this paper is to describe main ideas and properties of the SCR and clearly to describe three mutually complementary algorithms of the SCR that are presented in the form maximally suited for practical applications.