Systematic Differential Renormalization to All Orders

TL;DR

This paper introduces a systematic, all-orders differential renormalization method in coordinate space that simplifies the renormalization process by avoiding intermediate regularization and ensuring compliance with key physical principles.

Contribution

It provides a novel, systematic approach to differential renormalization applicable to all orders in perturbation theory, emphasizing coordinate space and subgraph organization.

Findings

Automatically yields renormalized amplitudes obeying RG equations

Ensures locality, unitarity, and Lorentz invariance in renormalization

Simplifies the renormalization process by bypassing intermediate regularization

Abstract

We present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynamn graphs written in coordinate space. After isolating every singularity. which appears in a bare diagram, we define a subtraction procedure which consists in replacing the core of the singularity by its renormalized form givenby a differential formula. The organizationof subtractions in subgraphs relies in Bogoliubov's formula, fulfilling the requirements of locality, unitarity and Lorentz invariance. Our method bypasses the use of an intermediate regularization andautomatically delivers renormalized amplitudes which obey renormalization group equations.