Self-energy of electrons in non-perturbative QED

TL;DR

This paper investigates models of charged particles interacting with a quantized radiation field, establishing non-perturbative bounds on their self-energies that reveal fundamental differences from perturbative predictions.

Contribution

It provides the first non-perturbative bounds on self-energies in models of charged particles coupled to a quantized field, highlighting differences from perturbation theory.

Findings

Bounds proportional to particle number for fermions

Sublinear bounds for bosons indicating binding

Non-perturbative results differ from perturbative predictions

Abstract

Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass renormalization. For $N$ fermions the bounds are proportional to $N$, but for bosons they are sublinear, which implies `binding', and hence that `free' bosons are never free. Both `relativistic' and non-relativistic kinematics are considered. Our bounds are non-perturbative and differ significantly from the predictions of perturbation theory.