Geometric interpretation of the Poisson structure in affine Toda field theories

1996/06/27 by Benjamin Enriquez, Enriquez, Benjamin, Edward Frenkel +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9606023

32 pages, AMSLATEX

openalex publication_date 1996/06/27 · arxiv created 1996/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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