6533b831fe1ef96bd1298e09

RESEARCH PRODUCT

Classical and Quantum Nonultralocal Systems on the Lattice

Alexey SevostyanovMichael Semenov-tian-shanskyMichael Semenov-tian-shansky

subject

PhysicsPoisson bracketNonlinear systemPure mathematicsNonlinear Sciences::Exactly Solvable and Integrable SystemsSigma modelPoisson manifoldLattice (order)Quantum mechanicsMonodromy matrixQuantumPoisson algebra

description

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 and is applied to the nonlinear sigma model problem.

yearjournalcountryeditionlanguage
1997-01-01
https://doi.org/10.1007/978-1-4612-2434-1_17