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    Disciplines / Research questions

    Physics

    691 research topics · 2739 questions

    Yang–Baxter Scattering Consistency1 questions

    1. General construction and classification of set-theoretical reflection maps, and the Poisson–Lie dynamics of their transfer maps

    Yang–Baxter algebra3 questions

    1. Completeness, norm formulae, and extension to the full non-symmetric Fock space for the non-symmetric Yang–Baxter algebra of the quantum nonlinear Schrödinger model

      Open for about 13 years

    2. Completeness, equivalence, and thermodynamic-limit structure of the Yang-Baxter-algebra Bethe-like systems for the XXZ chain with non-diagonal twisted and open boundaries

      Open for about 19 years

    3. Exact relation counts and prolongation-sequence periodicity for quadratic algebras of left-nondegenerate idempotent sets (Questions 4.12 and 6.12 of Gateva-Ivanova-Majid)

      Open for about 2 years
    Yang–Yang Thermodynamics1 questions

    1. Microscopic origin and single-shot interpretation of the density-grain statistics in the exactly solved one-dimensional Bose gas

    Yangian2 questions

    1. Explicit formula for the unitriangular factor R−(s)\mathcal{R}^-(s) of the Yangian universal RR-matrix beyond sl2\mathfrak{sl}_2, and algebra-level lift of its cocycle identity

      Open for about 7 years

    2. Quantum Yangian double and universal R-matrix for the centrally extended psu(2∣2)⋉C3\mathfrak{psu}(2|2)\ltimes\mathbb{C}^3 algebra underlying the AdS5_5/CFT4_4 S-matrix

      Open for about 14 years
    Yangian Representation Theory and Solving Nonlinear Models2 questions

    1. Quantum-algebraic (Yangian-type) symmetry underlying the non-difference-form 6-vertex B and 8-vertex B solutions of the Yang-Baxter equation

      Open for about 6 years

    2. Yang–Baxter integrability of the three-dimensional quantum crystal-melting Hamiltonian (dynamics of plane partitions)

      Open for about 18 years
    Zamolodchikov Three-Dimensional Model2 questions

    1. Elliptic completion of the tetrahedral Zamolodchikov algebra program for the fermionic Bazhanov-Stroganov R-operator: interacting extensions and the non-ultralocal continuum limit

    2. 3D origin of Shastry's R-matrix: deriving the Hubbard-model R-matrix from the Zamolodchikov model and uniformising the full tetrahedron equation

    Zamolodchikov–Faddeev Algebra4 questions

    1. Fock representations of Zamolodchikov–Faddeev algebras over involutive R-matrices: dependence on the R-matrix and scaling limits of integrable QFTs

    2. Positivity conjecture and q→0q\to0 crystal-limit identification for the qq-boson Zamolodchikov-Faddeev representation of the Uq(An(1))U_q(A^{(1)}_n) zero-range process

    3. Classification of Zamolodchikov–Faddeev algebra transformations for quantum quenches in interacting integrable quantum field theories and the first-principles construction of the quench initial state

    4. Completing the exact solution of open multi-species exclusion processes with integrable boundaries

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