Coulomb's law modification in nonlinear and in noncommutative electrodynamics

TL;DR

This paper investigates how Coulomb's law is modified in nonlinear Born-Infeld and noncommutative U(1) gauge theories, revealing long-range corrections in Born-Infeld but preserving Coulomb behavior in noncommutative electrodynamics.

Contribution

It provides a comparative analysis of Coulomb potential modifications in Born-Infeld and noncommutative electrodynamics using gauge-invariant variables.

Findings

Born-Infeld electrodynamics exhibits a $1/r^5$ correction to Coulomb potential.

Noncommutative electrodynamics maintains Coulomb potential at order $e^2$.

Long-range corrections are specific to nonlinear modifications of electrodynamics.

Abstract

We study the lowest-order modifications of the static potential for Born-Infeld electrodynamics and for the $\theta$-expanded version of the noncommutative U(1) gauge theory, within the framework of the gauge-invariant but path-dependent variables formalism. The calculation shows a long-range correction ($1/r^5$-type) to the Coulomb potential in Born-Infeld electrodynamics. However, the Coulomb nature of the potential (to order $e^2$) is preserved in noncommutative electrodynamics.