We re-examine Quantum Electrodynamics (QED) with massless electron as
a finite quantum field theory as advocated by Gell-Mann-Low, Baker-Joh
nson, Adler, Jackiw and others. We analyze the Dyson-Schwinger equatio
n satisfied by the massless electron in finite QED and conclude that t
he theory admits no nontrivial eigenvalue for the fine structure const
ant.