Classical and Quantum Nonultralocal Systems on the Lattice

A.V.Sevostyanov (Universite de Bourgogne; M.A.Semenov-Tian-Shansky; Steklov Mathematical Institute)

Classical and Quantum Nonultralocal Systems on the Lattice

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arxiv hep-th/9509029 v5 pith:YHA3K3K7 submitted 1995-09-07 hep-th

M.A.Semenov-Tian-Shansky , A.V.Sevostyanov (Universite de Bourgogne , Steklov Mathematical Institute) This is my paper · ORCID

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keywords algebrasnonultralocalsystemslatticepoissonquantumtechniqueapplied

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We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for these systems are constructed.For some class of such algebras an ultralocalization procedure is proposed.The technique of the modified Bethe-Anzatz for these algebras is developed.This technique is applied to the nonlinear sigma model problem.

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Ultralocal Lax connection for para-complex $\mathbb{Z}_T$-cosets
hep-th 2019-09 conditional novelty 7.0 of 10

Classical sigma-models on para-complex Z_T-cosets admit an ultralocal, gauge-invariant Lax connection whose light-cone components Poisson-commute, extending earlier results for hermitian symmetric spaces.

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