The Complete Solution of the Classical SL(2,R)/U(1) Gauged WZNW Field Theory

TL;DR

This paper provides a complete classical solution for the SL(2,R)/U(1) gauged WZNW model, including explicit solutions, symplectic structure, and transformations, setting the stage for exact quantization.

Contribution

It explicitly solves the classical equations of motion for the SL(2,R)/U(1) gauged WZNW model and derives the symplectic structure and transformations for quantization.

Findings

Explicit general solution of classical equations of motion.

Calculation of the symplectic structure via Gelfand-Dikii equation.

Transformation to canonical free fields and Bäcklund transformation.

Abstract

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local B\"acklund transformation. These calculations prepare the theory for an exact canonical quantization.