| Summary: | 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 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/L3 correction to the Coulomb potential, in contrast to the 1/L5 correction of the usual Born–Infeld theory.
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