The Nonlinear Schrodinger Equation on the Half Line
High Energy Physics - Theory
2009-10-31 v1 Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
solv-int
Abstract
The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag-Ruelle framework, suitably generalized to the case of broken translation invariance in space.
Cite
@article{arxiv.hep-th/9811188,
title = {The Nonlinear Schrodinger Equation on the Half Line},
author = {M. Gattobigio and A. Liguori and M. Mintchev},
journal= {arXiv preprint arXiv:hep-th/9811188},
year = {2009}
}
Comments
Tex file, no figures, 32 pages