The Relationship between Bare and Renormalized Couplings in Scalar Electrodynamics

TL;DR

This paper demonstrates how the renormalization group can sum divergent series in scalar electrodynamics, relating bare and renormalized couplings through dimensional regularization.

Contribution

It introduces a method to sum leading and next-to-leading pole contributions in the series expansion of couplings using the renormalization group.

Findings

Renormalization group effectively sums divergent series in scalar electrodynamics.

Explicit relations between bare and renormalized couplings are derived.

Method applicable to theories with multiple couplings.

Abstract

When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading pole etc. contributions to these sums in scalar electrodynamics (or any theory with multiple couplings.)