On the quantum KP hierarchy and its relation to the non-linear Schr\"odinger equation
High Energy Physics - Theory
2009-10-22 v1
Abstract
We establish a relation between the classical non-linear Schr\"odinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable models is discussed.
Keywords
Cite
@article{arxiv.hep-th/9208013,
title = {On the quantum KP hierarchy and its relation to the non-linear Schr\"odinger equation},
author = {M. D. Freeman and P. West},
journal= {arXiv preprint arXiv:hep-th/9208013},
year = {2009}
}
Comments
16 pages, KCL-TH-92-2