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

TL;DR

The paper introduces self-consistent renormalization (SCR), a method that preserves formal relations between divergent and regularized Feynman amplitudes, applicable to various quantum field theories, and provides practical algorithms for its implementation.

Contribution

It presents the SCR method as a unified approach to renormalization, capable of handling both renormalizable and nonrenormalizable theories with practical algorithms.

Findings

SCR maintains formal relations between divergent and regularized amplitudes.

SCR is applicable to theories with symmetries, Ward identities, and anomalies.

The paper provides three practical algorithms for SCR implementation.

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.