Introduction to Yangian in Physics

Mo-lin Ge; Kang Xue; Yiwen Wang

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Introduction to Yangian in Physics

Mo-lin Ge·Kang Xue·Yiwen Wang

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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 $gl(2)$ 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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Mo-lin Ge, Kang Xue, Yiwen Wang. 1995-09-15. Introduction to Yangian in Physics. https://arxiv.org/abs/cond-mat/9509090

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