2015/02/13 by Sh. Khachatryan, Álvaro Antônio Bandeira Ferraz, A. Ferraz +7 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Commutative property #FOS: Physical sciences #Geometry #Integrable system #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear system #Particle physics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #Scattering #Soliton #Statistical Mechanics (cond-mat.stat-mech) #Tetrahedron #Theoretical physics #Transfer matrix #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1502.04055
published in arXiv (Cornell University) (Cornell University) · 5 pages, 4 figures
arxiv created 2015/02/13 · openalex publication_date 2015/02/13 · arxiv updated 2015/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.