Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra

Abstract

The Poisson brackets for non-linear σ-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.

Keywords

• Classical exchange algebra
• Quantum group
• Non-linear σ-model
• Poisson structure