N-loop Treatment of Overlapping Diagrams by the Implicit Regularization Technique

TL;DR

This paper extends the Implicit Regularization Technique (IRT) to handle overlapping divergent loops algebraically in perturbative renormalization, demonstrating its potential for gauge theories.

Contribution

It introduces a generalization of IRT for perturbative renormalization, specifically addressing overlapping divergences algebraically.

Findings

IRT successfully applied to overlapping divergences

Connection established between renormalization and counterterms

IRT shows promise for gauge theory renormalization

Abstract

We show how the Implicit Regularization Technique (IRT) can be used for the perturbative renormalization of a simple field theoretical model, generally used as a test theory for new techniques. While IRT has been applied successfully in many problems involving symmetry breaking anomalies and nonabelian gauge groups, all at one loop level, this is the first attempt to a generalization of the technique for perturbative renormalization. We show that the overlapping divergent loops can be given a completely algebraic treatment. We display the connection between renormalization and counterterms in the Lagrangian. The algebraic advantages make IRT worth studying for perturbative renormalization of gauge theories.