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arXiv · hep-th/9710039

Algebraic Quantization of Integrable Models in Discrete Space-time

L. D. Faddeev·A. Yu. Volkov
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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.

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L. D. Faddeev, A. Yu. Volkov. 1997-10-08. Algebraic Quantization of Integrable Models in Discrete Space-time. https://arxiv.org/abs/hep-th/9710039

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