JAN JERZY SLAWIANOWSKI
Generalized BornInfeld and other essential nonlinearities
It turns out that the traditional BornInfeld nonlinear electrodynamics is but a special case of some more general promising pattern based on convincing differentialgeometric and grouptheoretic principles.There exist some interesting links to the theory of minimal surfaces and string models.Some fieldtheoretic models based on this pattern are suggested,in particular,the tetrad (generally
nleg) 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 BornInfeld structure of the resulting fieldtheoretic model.Some related dynamical models suggest new ideas concerning nonlinearity in quantum mechanics.
