Eur. Phys. J. C (2014) 74: 3182
https://doi.org/10.1140/epjc/s10052-014-3182-y

Regular Article - Theoretical Physics

Remarks on nonlinear electrodynamics

¹ Departmento de Física and Centro Científico-Tecnológico de Valparaíso, Universidad Técnica Federico Santa María, Valparaíso, Chile
² Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, RJ, Brazil

^* e-mail: patricio.gaete@usm.cl

Received: 21 August 2014
Accepted: 12 November 2014
Published online: 26 November 2014

Abstract

We consider both generalized Born–Infeld and exponential electrodynamics. The field energy of a point-like charge is finite only for Born–Infeld-like electrodynamics. However, both Born–Infeld-type and exponential electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range (-type) corrections to the Coulomb potential. Once again, for their noncommutative versions, the interaction energy is ultraviolet finite.