A reformulation of the Born-Infeld electrodynamics

Abstract

The electrodynamics proposed by Born & Infeld in 1934 differs from the Maxwell electrodynamics for very strong fields and gives a finite total energy for the field around a point charge. At that time not much was known about the dynamical theory of fields, and recent developments of this subject enable one to give a better formulation of the Born-Infeld theory. The basis is a comprehensive action principle that determines both the field equations and the equations of motion of charged particles. From this action principle a Hamiltonian formulation is obtained, the various Hamiltonian constraints being worked out. The classical theory is found to be completely satisfactory, but difficulties arise with the passage to the quantum theory, which appear to be insoluble with present methods of quantization.