Algebraic Quantization of Integrable Models in Discrete Space-time

1997/10/04 by L. D. Faddeev, Faddeev, L. D., A. Yu. Volkov +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9710039

22 pages, LATEX2e, misprints corrected

openalex publication_date 1997/10/04 · arxiv created 1997/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• How Algebraic Bethe Ansatz works for integrable model

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