 923 Bordemann M., Forger M., Laartz J., Schaeper U.
 {The LiePoisson Structure of Integrable Classical NonLinear Sigma
Models
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Jan 27, 92

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Abstract. The canonical structure of classical nonlinear sigma models on Riemannian
symmetric spaces, which constitute the most general class of classical
nonlinear sigma models known to be integrable, is shown to be governed by
a fundamental Poisson bracket relation that fits into the $r$$s$matrix
formalism for nonultralocal integrable models first discussed by Maillet.
The matrices $r$ and $s$ are computed explicitly and, being field dependent,
satisfy fundamental Poisson bracket relations of their own, which can be
expressed in terms of a new numerical matrix~$c$. It is proposed that
all these Poisson brackets taken together are representation conditions
for a new kind of algebra which, for this class of models, replaces the
classical YangBaxter algebra governing the canonical structure of ultralocal
models. The Poisson brackets for the transition matrices are also computed,
and the notorious regularization problem associated with the definition of
the Poisson brackets for the monodromy matrices is discussed.
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