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.
Classical and Quantum Nonultralocal Systems on the Lattice
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abstract
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
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.