Summation of Higher Order Effects using the Renormalization Group Equation

TL;DR

This paper explores how the renormalization group (RG) equation can be used to sum higher order effects in quantum field theory, emphasizing scheme dependence and applications to thermal field theory and scalar electrodynamics.

Contribution

It introduces a method using the RG equation and characteristics to sum higher order effects, analyzing scheme dependence and specific applications in field theory.

Findings

RG scheme affects higher order corrections

Method of characteristics effectively sums higher order effects

Applications to free energy and effective potential

Abstract

The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is payed to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed, and is used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling and the effective potential in massless scalar electrodynamics.