Self-Similar Structure of Loop Amplitudes and Renormalization

TL;DR

This paper explores the self-similar structure of loop amplitudes in quantum field theory, proposing a recursive, scale-dependent approach to amplitude generation and renormalization that ensures finite results and offers an alternative to traditional methods.

Contribution

It introduces a recursive, scale-dependent framework for loop amplitude renormalization, viewing amplitudes as effective couplings within the S-matrix, and provides a bottom-up proof of renormalization.

Findings

A renormalized amplitude acts as an effective, observable coupling.

The method guarantees no subamplitude divergence in high-order loops.

Provides an alternative recursive approach to traditional renormalization.

Abstract

We study the self-similar structure of loop amplitudes in quantum field theory and apply it to amplitude generation and renormalization. A renormalized amplitude can be regarded as an effective coupling that recursively appears within another loop. It is best described as a vertex function from the effective action. It is a scale-dependent, finite, parametrically small and observable quantity appearing in the S-matrix. Replacing a tree-level coupling with a loop amplitude provides a systematic method of generating high-order loop amplitudes, guaranteeing no subamplitude divergence. This method also provides an alternative bottom-up proof to the traditional top-down recursive renormalization of general amplitudes.