Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams

TL;DR

This paper presents a systematic implementation of Implicit Regularization (IReg) for multi-loop Feynman diagrams, ensuring invariance and consistency in quantum field theory calculations.

Contribution

The work automates the identification of subtraction terms in IReg, demonstrating its respect for fundamental symmetries and its ability to isolate divergences using basic integrals.

Findings

IReg respects unitarity, locality, and Lorentz invariance.

The method effectively displays divergences in multi-loop amplitudes.

Momentum routing invariance is conjectured as a fundamental symmetry.

Abstract

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.