Physics of Renormalization Group Equation in QED

TL;DR

This paper argues that the renormalization group equation in QED only captures finite size effects and is not suitable for continuum limit treatments, challenging common assumptions in lattice gauge theory.

Contribution

It clarifies the physical origin of the RG equation in QED and critiques its application to lattice gauge theory continuum limits.

Findings

RG equation describes finite size effects in QED

Application to continuum limit of lattice gauge theory is invalid

Wilson's action results remain unphysical in this context

Abstract

It is shown that the renormalization group (RG) equation in QED can only describe the finite size effects of the system. The RG equation is originated from the response of the renormalized coupling constant for the change of the system size $L$. The application of the RG equation to the continuum limit treatment of the lattice gauge theory, therefore, does not make sense, and the well-known unphysical result of the lattice gauge theory with Wilson's action cannot be remedied any more.