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During the 1990s there was a revival of interest on Born-Infeld theory and its nonabelian extensions as they were found in some limits of string theory.
A field theory showing this property is usually called completely exceptional and Born-Infeld theory is the only completely exceptional regular nonlinear electrodynamics.
Finally (and more technically) Born-Infeld theory can be seen as a covariant generalization of Mie's theory, and very close to Einstein's idea of introducing a nonsymmetric metric tensor with the symmetric part corresponding to the usual metric tensor and the antisymmetric to the electromagnetic field tensor.