JAN JERZY SLAWIANOWSKI
Generalized Born-Infeld and other essential nonlinearities
It turns out that the traditional Born-Infeld nonlinear electrodynamics is but a special case of some more general promising pattern based on convincing differential-geometric and group-theoretic principles.There exist some interesting links to the theory of minimal surfaces and string models.Some field-theoretic models based on this pattern are suggested,in particular,the tetrad (generally
n-leg) approaches to gravitation invariant under the action of the internal group GL(4,R) (generally GL(n,R)).It turns out that the demand of affine invariance in a sense implies generalized Born-Infeld structure of the resulting field-theoretic model.Some related dynamical models suggest new ideas concerning nonlinearity in quantum mechanics.
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