Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra

TL;DR

This paper constructs a Killing scalar in non-linear sigma models on G/H that transforms irreducibly under Killing vectors and demonstrates it satisfies the classical exchange algebra, advancing understanding of their algebraic structure.

Contribution

It introduces a Killing scalar in arbitrary representations of G for non-linear sigma models on G/H and proves it obeys the classical exchange algebra.

Findings

Killing scalar transforms irreducibly under Killing vectors.

Killing scalar satisfies the classical exchange algebra.

Poisson brackets are established on the light-like plane.

Abstract

The Poisson brackets for non-linear sigma models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra.