JAN SLAWIANOWSKI

BORN-INFELD NONLINEARITY.OLD AND NEW IDEAS

Traditional Born-Infeld model was motivated by difficulties of Maxwell electrodynamics like the infinite electromagnetic mass of point charges,inependence of field equations and equations of motion,and also by certain generally-relativistic ideas.It has some canonical features among all possible nonlinear electrodynamics models;it is not "nonlinearity as any other".After some primary enthusiasm there was however a period of disappointment implied by the success of quantum field theory and renormalization.They seemed to make the Born-Infeld problem superfluous.Recently we witness some come-back of Born-Infeld ideas (in a modified form) in connection with string and p-branes theory,geometry of minimal surfaces and some new models of field theory.We discuss the general structure of modified Born-Infeld- type nonlinearity in a pure nonlinear science as such,and also within the context of field theory,differential geometry,continuum mechanics and perhaps even nonlinear quantum mechanics.It turns out that the modified Born-Infeld nonlinearity may establish some link between internal symmetris and the general covariance.It also sheds new light onto the theory of variational principles.