Introduction to Yangian in Physics

Details Introduction to Yangian in Physics Introduction to Yangian in Physics

1995-09-15

arxiv.org/abs/cond-mat/9509090v1

Physics

Condensed Matter

41 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. Invited talk presented at Second Pacific Physics Winter Sch

Scientific paper

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 $gl(2)$ are given through solving the RTT relations. It contains the Drinfeld's $Y(sl(2))$, $Y(sl(n))$ 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 $q$-affine algebra.

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