Introduction to Yangian in Physics
Abstract
This is an introduction to the physical pictures of {\em Yangian} symmetry. All the discussions are based on the RTT relations which have been known to be related to the Hamiltonian formulations for quantum integrable systems. The explicit calculations of {\em Yangian} associated with are given through solving the RTT relations. It contains the Drinfeld's , and Heisenberg type of Hopf algebras. Examples are emphasized to show the physical pictures, such as Hubbard model, Haldane-Shastry model, Long-range interaction models and Goryachev-Chaplygin(G-C) gyrostat. The example of the trigonometric extension of G-C gyrostat are also shown that leads to the non-commutative geometry naturally on the basis of the truncated -affine algebra.
Cite
@article{arxiv.cond-mat/9509090,
title = {Introduction to Yangian in Physics},
author = {Mo-lin Ge and Kang Xue and Yiwen Wang},
journal= {arXiv preprint arXiv:cond-mat/9509090},
year = {2007}
}
Comments
41 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. Invited talk presented at Second Pacific Physics Winter School. For hard copy, write to Prof. Mo-lin GE, Nankai Institute of Mathematics. Do not send emails to this computer account