Born-Infeld electrodynamics in very special relativity

In this work we discuss the properties of a modified Born-Infeld electrodynamics in the framework of very special relativity (VSR). This proposal allows us to study VSR mass effects in a gauge-invariant context of nonlinear electrodynamics. It is analyzed in detail the electrostatic solutions for two different cases, as well as the VSR dispersion relations are found to be of a \emph{massive} particle with nonlinear modifications. Afterwards, the field energy and static potential are computed, in the latter we find from the VSR contribution a novel long-range $1/L^3$ correction to the Coulomb potential, in contrast to the $1/L^5$ correction of the usual Born-Infeld theory.