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Geometric interpretation of the Poisson structure in affine Toda field theories

Benjamin Enriquez·Edward Frenkel
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Abstract

We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of fields, containing ``half screening charges'' and ``half integrals of motions''. In addition to local terms, the Poisson brackets contain nonlocal terms related to trigonometric r-matrices.

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Benjamin Enriquez, Edward Frenkel. 1996-07-02. Geometric interpretation of the Poisson structure in affine Toda field theories. https://arxiv.org/abs/q-alg/9606023

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