Singular structure of the QED effective action

TL;DR

This paper analyzes the structure of the QED effective action, revealing that it consists of a regular part matching perturbation theory and a singular part preventing the electromagnetic interaction from being turned off.

Contribution

It demonstrates the singular nature of the QED effective action, showing the impossibility of completely switching off electromagnetic interactions within quantum field theory.

Findings

Regular part matches Feynman perturbation series

Singular part has an essential singularity at zero coupling

Electromagnetic interaction cannot be fully turned off

Abstract

The equations for the QED effective action derived in \cite{fm} are considered using singular perturbation theory. The effective action is divided into regular and singular (in coupling constant) parts. It is shown that expression for the regular part coincides with usual Feynman perturbation series over coupling constant, while the remainder has essential singularity at the vanishing coupling constant: $e\rightarrow 0$. This means that in the frame of quantum field theory it is impossible "to switch off" electromagnetic interaction in general and pass on to "free electron".