No Eigenvalue in Finite Quantum Electrodynamics

TL;DR

This paper investigates finite quantum electrodynamics with massless electrons, analyzing the Dyson-Schwinger equation and concluding that the theory admits no nontrivial eigenvalue for the fine structure constant.

Contribution

It provides a re-examination of finite QED with massless electrons, showing the absence of nontrivial eigenvalues for the fine structure constant.

Findings

No nontrivial eigenvalue for the fine structure constant in finite QED.

Re-examination of Dyson-Schwinger equations in this context.

Supports the view that finite QED with massless electrons has unique properties.

Abstract

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