Causal Poisson Brackets of the SL(2,R) WZNW Model and its Coset Theories

TL;DR

This paper derives non-equal time Poisson brackets for the SL(2,R) WZNW model and its coset theories using Hamiltonian reduction, providing a detailed algebraic framework for these models.

Contribution

It introduces a method to obtain non-equal time Poisson brackets for the SL(2,R) WZNW model and its cosets from basic chiral brackets, advancing the algebraic understanding.

Findings

Derived non-equal time Poisson brackets for SL(2,R) WZNW model

Extended brackets to coset theories via Hamiltonian reduction

Provided a consistent algebraic structure for these models

Abstract

From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2,R) WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian reduction we deduce the corresponding brackets for its coset theories.