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

TL;DR

This paper introduces a polarization of gauge transformation Lie algebras on the light-cone in 3+1 dimensions, extending affine Kac-Moody algebra concepts to higher dimensions and enabling a new highest weight theory.

Contribution

It generalizes the polarization of affine Kac-Moody algebras to 3+1 dimensions, facilitating a new approach to gauge theories on the light-cone.

Findings

Polarization of gauge transformation algebras on the light-cone.

Extension of highest weight theory to 3+1 dimensions.

Framework for future light-cone quantization methods.

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.