Finite field-energy and interparticle potential in logarithmic electrodynamics

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 (1/r5-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. (orig.)