Algebraic Quantization of Integrable Models in Discrete Space-time

Abstract

Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum discrete-discrete models. We observe how this idea applies to a difference-difference counterpart of the Liouville equation. We produce explicit forms of of its evolution operator for the two natural space-time coordinate systems. We discover that discrete-discrete models inherit crucial features of their continuous-time parents like locality and integrability while the new-found algebraic transparency promises a useful progress in some branches of Quantum Inverse Scattering Method.

22 pages, LATEX2e, misprints corrected

References in corpus (4)

• How Algebraic Bethe Ansatz works for integrable model
• Abelian Current Algebra and the Virasoro Algebra on the Lattice
• Hirota equation as an example of integrable symplectic map
• Current-Like Variables in Massive and Massless Integrable Models

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• The Quantum Gravity Disk: Discrete Current Algebra
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• Lattice two-point functions and conformal invariance