Strong, Random field behavior of the Euclidean Dirac propagator

TL;DR

This paper investigates the behavior of the Euclidean Dirac propagator in strong electromagnetic fields within quantum electrodynamics, revealing it vanishes in the strong field limit and discussing implications for decoupling in the electroweak model.

Contribution

It demonstrates that the Euclidean Dirac propagator vanishes in the strong field limit, providing new insights into QED's behavior under intense fields and its decoupling from the electroweak model.

Findings

The Dirac propagator vanishes in the strong field limit.

The effective action is controlled by the Euclidean Dirac propagator.

Implications for decoupling of QED from the electroweak model.

Abstract

The one-loop effective action of quantum electrodynamics in four dimensions is shown to be controlled by the Euclidean Dirac propagator $G$ in a background potential. After separating the photon self-energy and photon-photon scattering graphs from the effective action the remainder is known to be the logarithm of an entire function of the electric charge of order 4 under mild regularity assumptions on the potential. This input together with QED's lack of an ultrastable vacuum constrain the strong field behavior of $G$. It is shown that $G$ vanishes in the strong field limit. The relevance of this result to the decoupling of QED from the remainder of the electroweak model for large amplitude variations of the Maxwell field is discussed.