Run-away solutions in relativistic spin 1/2 quantum electrodynamics

TL;DR

This paper reviews run-away solutions in quantum electrodynamics, showing relativistic spin 1/2 QED avoids them due to less singular high-energy behavior, but potential anomalies could introduce new run-aways at very high energy scales.

Contribution

It demonstrates that relativistic spin 1/2 QED does not exhibit classical run-away solutions and discusses conditions under which new run-aways might occur due to anomalies.

Findings

Relativistic spin 1/2 QED lacks classical run-away solutions.

Potential anomalies could induce new run-aways at exponentially high energies.

High-energy behavior influences the presence of run-away solutions.

Abstract

The existence of run-away solutions in classical and non-relativistic quantum electrodynamics is reviewed. It is shown that the less singular high energy behavior of relativistic spin 1/2 quantum electrodynamics precludes an analogous behavior in that theory. However, a Landau-like anomalous pole in the photon propagation function or in the electron-massive photon foward scattering amplitude would generate a new run-away, characterized by an energy scale omega ~ m_e exp (1/alpha). This contrasts with the energy scale omega ~ (m_e/alpha) associated with the classical and non-relativistic quantum run-aways.