Yangian symmetry in the Nonlinear Schrödinger hierarchy
نویسندگان
چکیده
We study the Yangian symmetry of the multicomponent Quantum Nonlinear Schrödinger hierarchy in the framework of the Quantum Inverse Scattering Method. We give an explicit realization of the Yangian generators in terms of the deformed oscillators algebra which naturally occurs in this framework. LAPTH-733/99 IFUP-TH 24/99 CRM-2608 hep-th/9905105 [email protected] [email protected] [email protected] [email protected]
منابع مشابه
Deformed oscillators algebra formulation of the Nonlinear Schrödinger hierarchy and of its symmetry
We present a self-contained formulation of the Nonlinear Schrödinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y (glN ) and finite W (glpN , N.glp) algebras is also illustrated in this framework. To be published in the proceedings of QGIS-99, Prague, June 17-19 1999 July 1999 LAPTH-743/99-Conf hep-th/9907218 [email protected]...
متن کاملLax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation
We consider a version of the non-linear Schrödinger 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 construc...
متن کاملY(so(5)) symmetry of the nonlinear Schrödinger model with four-components
The quantum nonlinear Schrödinger(NLS) model with four-component fermions exhibits a Y (so(5)) symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel’d formula and furthermore, the RTT relation with the general form of rational R-matrix given by Yang-Baxterization associated with so(5) algebraic structure.
متن کاملAffine Lie group approach to a derivative nonlinear Schrödinger equation and its similarity reduction
The generalized Drinfel’d-Sokolov hierarchies studied by de Groot-HollowoodMiramontes are extended from the viewpoint of Sato-Wilson dressing method. In the A (1) 1 case, we obtain the hierarchy that include the derivative nonlinear Schrödinger equation. We give two types of affine Weyl group symmetry of the hierarchy based on the Gauss decomposition of the A (1) 1 affine Lie group. The fourth ...
متن کاملW-symmetry, topological vertex and affine Yangian
We discuss the representation theory of the non-linear chiral algebra W1+∞ of Gaberdiel and Gopakumar and its connection to the Yangian of û(1) whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of W1+∞ are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999