Increase of the binding energy of an electron by coupling to a photon field

TL;DR

Coupling an electron to a quantized photon field increases its binding energy, with specific conditions on the coupling strength and parameters provided.

Contribution

This work demonstrates that electron binding energy increases upon coupling to a photon field and supplies explicit parameter bounds for this effect.

Findings

Binding energy increases with photon coupling.

Explicit bounds on coupling constant and parameters.

Quantitative radiative correction estimates.

Abstract

We look at an electron in the field of an arbitrary external potential $V$, such that the Schr\"odinger operator $p^2 + V$ has at least one eigenvalue, and show that by coupling to a quantized radiation field the binding energy increases, at least for small enough values of the coupling constant $\alpha$. Moreover, we provide concrete numbers for $\alpha$, the ultraviolet cut-off $\Lambda$, and the radiative correction for which our procedure works.