Eur. Phys. J. C (2014) 74: 2816
https://doi.org/10.1140/epjc/s10052-014-2816-4

Regular Article - Theoretical Physics

Finite field-energy and interparticle potential in logarithmic electrodynamics

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

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

Received: 23 December 2013
Accepted: 6 March 2014
Published online: 18 March 2014

Abstract

We pursue an investigation of logarithmic electrodynamics, for which the field energy of a point-like charge is finite, as happens in the case of the usual Born–Infeld electrodynamics. We also show that, contrary to the latter, logarithmic electrodynamics exhibits the feature of birefringence. Next, we analyze the lowest-order modifications for both logarithmic electrodynamics and for its non-commutative version, within the framework of the gauge-invariant path-dependent variables formalism. The calculation shows a long-range correction (-type) to the Coulomb potential for logarithmic electrodynamics. Interestingly enough, for its non-commutative version, the interaction energy is ultraviolet finite. We highlight the role played by the new quantum of length in our analysis.