Approximate Born-Infeld Effects on the Relativistic Hydrogen Spectrum

TL;DR

This paper investigates the effects of Born-Infeld nonlinear electrodynamics on the relativistic hydrogen spectrum using the Dirac equation, establishing bounds on the theory's fundamental constant based on spectral analysis.

Contribution

It extends previous non-relativistic analyses by incorporating the Dirac equation, providing tighter bounds on the Born-Infeld parameter and assessing its physical viability.

Findings

The relativistic spectrum constrains the Born-Infeld constant to be below previous estimates.

Dirac equation corrections are minor but important for precise bounds.

The study narrows the parameter space where Born-Infeld electrodynamics could be physically relevant.

Abstract

The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born-Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born-Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well below the original value proposed by Born. This work extends the original Schrodinger spectrum from Carley and Kiessling (2006) [1] for the self-field correction, and shows that using the Dirac equation introduces minor corrections - but also gives access to a range for the fundamental constant that is below that attainable from non-relativistic considerations.