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Teoreticheskaya i Matematicheskaya Fizika, 1983, Volume 56, Number 3, Pages 323–343
(Mi tmf2216)
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This article is cited in 29 scientific papers (total in 30 papers)
Hamiltonian structures for integrable models of field theory
N. Yu. Reshetikhin, L. D. Faddeev
Abstract:
It is shown that for classical continuous integrable field theory models the Poisson
brackets, defined in $r$-matrix form, admit a simple geometrical interpretation in
terms of current algebra. In such an interpretation, the phase spaces of the models are integral manifolds of a standard symplectic structure on the current algebra. For discrete integrable systems, integral manifolds are constructed for discrete $r$-matrix brackets for rational r matrices associated with the classical Lie algebras. It is shown that in the discrete ease there is a multiplicative operation of averaging that makes it possible to obtain trigonometric and elliptic $L$ operators from rational operators. This averaging is explicitly performed for the single-pole $L$ operator associated with the algebra $\mathfrak{sl}(2)$.
Received: 15.02.1983
Citation:
N. Yu. Reshetikhin, L. D. Faddeev, “Hamiltonian structures for integrable models of field theory”, TMF, 56:3 (1983), 323–343; Theoret. and Math. Phys., 56:3 (1983), 847–862
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https://www.mathnet.ru/eng/tmf2216 https://www.mathnet.ru/eng/tmf/v56/i3/p323
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Abstract page: | 792 | Full-text PDF : | 278 | References: | 67 | First page: | 3 |
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