Quantum resolution of the nonlinear super-Schrodinger equation

Abstract

We introduce a Z_2-graded version of the nonlinear Schrodinger equation that includes one fermion and one boson at the same time. This equation is shown to possess a supersymmetry which proves to be itself part of a super-Yangian symmetry based on gl(1|1). The solution exhibits a super version form of the classical Rosales solution. Then, we second quantize these results, and give a Lax pair formulation (based on gl(2|1)) for the model.

20 pages, no figure

References in corpus (8)

• Fock Representations of Quantum Fields with Generalized Statistic
• Tests of Integrability of the Supersymmetric Nonlinear Schrodinger Equation
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• Supersymmetric Drinfeld-Sokolov reduction
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• The Nonlinear Schrodinger Equation on the Half Line
• Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation
• A Nonstandard Supersymmetric KP Hierarchy