The Nonlinear Schrodinger Equation and Conserved Quantities in the Deformed Parafermion and SL(2,R)/U(1) Coset Models

TL;DR

This paper explores the connection between the nonlinear Schrödinger hierarchy and certain coset models, revealing conserved quantities and quantization features that deepen understanding of integrable structures in these theories.

Contribution

It establishes a detailed relationship between NLS hierarchies and parafermion and SL(2,R)/U(1) models, including the construction of quantum Hamiltonians and conserved quantities.

Findings

Quantum NLS Hamiltonians are conserved in the models

Explicit construction of the first few quantum NLS Hamiltonians

Identification of features in the quantized free part similar to bosonized models

Abstract

The relationship between the nonlinear Schrodinger hierarchy and the parafermion and SL(2,R)/U(1) coset models, analogous to the relationship between the KdV hierarchy and the minimal models, is explained. To do this I first present an in depth study of a series of integrable hierarchies related to NLS, and write down an action from which any of these hierarchies, and the associated second Poisson bracket structures, can be obtained. In quantizing the free part of this action we find many features in common with the bosonized parafermion and SL(2,R)/U(1) models, and particularly it is clear that the quantum NLS hamiltonians are conserved quantities in these models. The first few quantum NLS hamiltonians are constructed.