Quantization of three-wave equations

Abstract

The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave equations. The quantized systems in discrete space-time may be understood as the regularized integrable quantum field theories. Integrability of the theories, and in particular the quantum tetrahedron equations for vertex operators, follow from the quantum auxiliary linear problems. Principal object of the lattice field theories is the Heisenberg discrete time evolution operator constructed with the help of vertex operators.