Vanishing of the Bare Coupling in Four Dimensions

TL;DR

This paper investigates the relationship between bare and renormalized coupling constants in four-dimensional quantum field theories, demonstrating that the bare coupling vanishes in the four-dimensional limit through all-orders summation.

Contribution

It introduces a new restructuring of the series relating bare and renormalized couplings and proves the vanishing of the bare coupling in four dimensions.

Findings

Bare coupling vanishes in four dimensions

All-orders summation of leading epsilon poles

Reorganization of the series relationship

Abstract

We examine two restructurings of the series relationship between the bare and renormalized coupling constant in dimensional regularization. In one of these restructurings, we are able to demonstrate via all-orders summation of leading and successive epsilon = 0 (dimensionality = 4) poles that the bare coupling vanishes in the dimension-4 limit.