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.