Optimal number of terms in QED series and its consequence in condensed matter implementations of QED

TL;DR

This paper estimates the optimal number of terms in the QED perturbation series to be around 5000, with fewer terms applicable in condensed matter systems like semiconductors and Weyl semimetals, highlighting limitations in graphene.

Contribution

It combines Dyson's argument with Chandrasekhar's limit to estimate the optimal QED series terms and explores implications for condensed matter systems.

Findings

Optimal QED series terms estimated at ~5000.

Condensed matter systems have fewer optimal terms (~80).

Perturbation theory is limited in graphene.

Abstract

In 1952 Dyson put forward a simple and powerful argument indicating that the perturbative expansions of QED are asymptotic. His argument can be related to Chandrasekhar's limit on the mass of a star for stability against gravitational collapse. Combining these two arguments we estimate the optimal number of terms of the QED series to be $3.1(137)^{3/2}\approx5000$. For condensed matter manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the optimal number of terms is around $80$ while in graphene the utility of the perturbation theory is severely limited.