Binding threshold for the Pauli-Fierz operator

TL;DR

This paper investigates how the binding threshold of the Pauli-Fierz operator behaves as the fine structure constant approaches zero, showing convergence to the Schrödinger operator's threshold.

Contribution

It establishes the convergence of the binding threshold for the Pauli-Fierz operator to that of the Schrödinger operator in the small alpha limit.

Findings

Binding threshold converges to Schrödinger operator threshold as alpha approaches zero.

Results apply to operators with short-range potentials.

Provides insights into quantum electrodynamics models at small coupling constants.

Abstract

For the Pauli-Fierz operator with a short range potential we study the binding threshold as a function of the fine structure constant $\alpha $ and show that it converges to the binding threshold for the Schr\"odinger operator in the small $\alpha$ limit.