The phase space of the Wess-Zumino-Witten model

TL;DR

This paper demonstrates the equivalence of covariant and Hamiltonian phase spaces in the Wess-Zumino-Witten model on a cylinder and derives its Poisson brackets, clarifying its geometric and algebraic structure.

Contribution

It proves the diffeomorphism between covariant and Hamiltonian phase spaces and explicitly computes the Poisson brackets for the model.

Findings

Covariant and Hamiltonian phase spaces are diffeomorphic.

Poisson brackets of the Wess-Zumino-Witten model are derived.

Provides geometric insight into the model's phase space structure.

Abstract

We prove that the covariant and Hamiltonian phase spaces of the Wess-Zumino-Witten model on the cylinder are diffeomorphic and we derive the Poisson brackets of the theory.