The Quantum Volterra Model and the Lattice Sine--Gordon System. -- Construction of the Baxter Q Operator and the Integrals of Motion

Abstract

We investigate the integrable structure of thequantum Volterra model, which is a discretization of theKorteweg--de Vries equation.Based on Sklyanin's method we derive the Baxter equation, and thenclarify a role of the “fundamental transfer matrix”.We show that the fundamental transfer matrix also generates theintegrals of motionfor a lattice analogue of the sine--Gordon system.