Non-abelian Harmonic Oscillators and Chiral Theories

TL;DR

This paper reveals that diverse physical theories, including harmonic oscillators and complex field models, share geometric features in their Hamiltonian formulation, characterized by chiral equations of motion enabling phase space decomposition.

Contribution

It identifies a unifying geometric structure in Hamiltonian formulations of various theories, from oscillators to field models, highlighting the role of chiral equations.

Findings

Shared geometric features in Hamiltonian formulations

Chiral equations enable phase space decomposition

Applicability to a wide class of physical models

Abstract

We show that a large class of physical theories which has been under intensive investigation recently, share the same geometric features in their Hamiltonian formulation. These dynamical systems range from harmonic oscillations to WZW-like models and to the KdV dynamics on $Diff_oS^1$. To the same class belong also the Hamiltonian systems on groups of maps. The common feature of these models are the 'chiral' equations of motion allowing for so-called chiral decomposition of the phase space.