Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom

TL;DR

This paper performs the first nonperturbative numerical calculations of the hydrogen atom spectrum using Born-Infeld nonlinear electrodynamics, providing bounds on the electromagnetic constant and comparing with empirical data.

Contribution

It introduces a nonperturbative numerical approach to calculate the hydrogen spectrum within Born-Infeld electrodynamics, offering new bounds on the theory's parameters.

Findings

Significant restrictions on the electromagnetic constant from empirical data

Rigorous bounds established for the hydrogen ground state energy

Assessment of Born's proposed value for the nonlinear constant

Abstract

We present the first nonperturbative numerical calculations of the nonrelativistic hydrogen spectrum as predicted by first-quantized electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also show rigorous upper and lower bounds on the ground state. When judged against empirical data our results significantly restrict the range of viable values of the new electromagnetic constant which is introduced by the Born-Infeld theory. We assess Born's own proposal for the value of his constant.