English

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