The Nonlinear Schrodinger Equation on the Half Line

Details The Nonlinear Schrodinger Equation on the Half Line The Nonlinear Schrodinger Equation on the Half Line

1998-11-20

arxiv.org/abs/hep-th/9811188v1

J.Math.Phys. 40 (1999) 2949-2970

Physics

High Energy Physics

High Energy Physics - Theory

Tex file, no figures, 32 pages

Scientific paper

10.1063/1.532738

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.

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