Quantum resolution of the nonlinear super-Schrodinger equation

Caudrelier, V. & Ragoucy, E. (2004). Quantum resolution of the nonlinear super-Schrodinger equation. International Journal of Geometric Methods in Modern Physics (ijgmmp), 19(10), pp. 1559-1577. doi: 10.1142/S0217751X0401804X

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Abstract

We introduce a Z2-graded version of the nonlinear Schr¨odinger 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(1j1). 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(2j1)) for the model.

Item Type: Article
Additional Information: Electronic version of an article published as V. CAUDRELIER and E. RAGOUCY, Int. J. Mod. Phys. A 19, 1559 (2004). DOI: 10.1142/S0217751X0401804X © copyright World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijmpa
Uncontrolled Keywords: Integrable systems, supersymmetry, ZF algebras
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/170

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