Landau Singularity and the Instability of Vacuum State in QED

TL;DR

This paper discusses how the Landau singularity in QED indicates vacuum instability, supported by theoretical arguments from stability of matter and weakly interacting fermion systems, without a rigorous proof.

Contribution

It offers a novel interpretation linking Landau singularity to vacuum instability in QED using theoretical insights from stability and fermion systems.

Findings

Landau singularity suggests vacuum instability in QED

Theoretical arguments support the link between singularity and instability

No rigorous proof provided, but strong theoretical support

Abstract

In this paper, we argue that the Landau singularity of the coupling constant in QED reflects the instability of vacuum state, in other words the perturbative ground state in QED.We do not have a rigorous mathematical proof. We rather provide strong arguments derived from the theory of stability of matter developed by Lieb et al on the hand and the theory of weakly interacting fermion systems developed by Feldman et al on the other hand.