Impossibility of Finite Charge Renormalization in Sixth Order

Abstract

Making use of a recent result obtained by Jackiw in the context of the renormalization group we examine the question of whether there exists the possibility of obtaining finite charge renormalization by means of an eigenvalue condition on the bare coupling constant. It is shown that to sixth order in ${e}_{0}$ a cancellation of the divergences encountered in perturbation theory cannot occur.