Current algebras and light-cone quantization in 3+1 dimensions

Abstract

A polarization of the Lie algebras $Map(C, G)$ of gauge transformations on the light-cone $C\subset\RM^4$ is introduced, using splitting of the initial data on $C$ for the wave operator to positive and negative frequencies. This generalizes the usual polarization of affine Kac-Moody algebras to positive and negative frequencies and paves the way to a generalization of the highest weight theory to the $3+1$ dimensional setting.