Particles and strings in a (2+1)-D integrable quantum model

Abstract

We give a review of some recent work on generalization of the Bethe ansatz in the case of $2+1$-dimensional models of quantum field theory. As such a model, we consider one associated with the tetrahedron equation, i.e. the $2+1$-dimensional generalization of the famous Yang--Baxter equation. We construct some eigenstates of the transfer matrix of that model. There arise, together with states composed of point-like particles analogous to those in the usual $1+1$-dimensional Bethe ansatz, new string-like states and string-particle hybrids.

References in corpus (4)

• Some eigenstates for a model associated with solutions of tetrahedron equation
• Bethe ansatz for the three-layer Zamolodchikov model
• Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1
• Quantum model of interacting ``strings'' on the square lattice

Cited by in corpus (3)

• Two-color solutions of set-theoretic tetrahedron equation and their cohomologies
• "Nonconstant cohomology" of Hietarinta's two-color solutions to four-simplex equation
• Three-dimensionalizing the eight-vertex model