Hirota equation as an example of integrable symplectic map

TL;DR

This paper develops a Hamiltonian formalism for Hirota's sine-Gordon model on a light-like lattice, constructs the quantum evolution operator, and proves the classical integrability of the associated finite-dimensional system.

Contribution

It introduces a Hamiltonian framework for Hirota's model, explicitly constructs the quantum evolution operator, and demonstrates classical integrability, advancing understanding of integrable symplectic maps.

Findings

Explicit quantum evolution operator constructed

Classical finite-dimensional system shown to be integrable

Hamiltonian formalism developed for Hirota's lattice model

Abstract

The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of the corresponding classical finite-dimensional system is established.