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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 (1/r⁵ -type) corrections to the Coulomb potential. Once again, for their noncommutative versions, the interaction energy is ultraviolet finite.
Gaete et al. (Sat,) studied this question.