Lax pair and super-Yangian symmetry of the non-linear super-Schr\"odinger equation
Caudrelier, V. ; Ragoucy, E.
arXiv, 0306115 / Harvested from arXiv
Text on arXiv
We consider a version of the non-linear Schr\"odinger equation with M bosons and N fermions. We first solve the classical and quantum versions of this equation, using a super-Zamolodchikov-Faddeev (ZF) algebra. Then we prove that the hierarchy associated to this model admits a super-Yangian Y(gl(M|N)) symmetry. We exhibit the corresponding (classical and quantum) Lax pairs. Finally, we construct explicitly the super-Yangian generators, in terms of the canonical fields on the one hand, and in terms of the ZF algebra generators on the other hand. The latter construction uses the well-bred operators introduced recently.
Publié le : 2003-06-06
Classification:  Mathematics - Quantum Algebra,  High Energy Physics - Theory,  Mathematical Physics,  81R12 
@article{0306115,
     author = {Caudrelier, V. and Ragoucy, E.},
     title = {Lax pair and super-Yangian symmetry of the non-linear
  super-Schr\"odinger equation},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306115}
}

Caudrelier, V.; Ragoucy, E. Lax pair and super-Yangian symmetry of the non-linear
  super-Schr\"odinger equation. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306115/