Related papers: Tetrahedron equation and cyclic quantum dilogarith…
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
We review and supplement the recent result by the authors on the reduction of the three dimensional $R$ (3d $R$) satisfying the tetrahedron equation to the quantum $R$ matrices for the $q$-oscillator representations of $U_q(D^{(2)}_{n+1})$,…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichm\"uller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of…
We formulate Shintani's invariant in terms of the cyclic quantum dilogarithm. Building on earlier results that expressed Shintani's invariant using the $q$-Pochhammer symbol, we show how the cyclic quantum dilogarithm naturally arises in…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
We solve a very classical problem motivated by considerations in quantum gravity: providing a description of the geometry of a Euclidean tetrahedron from the initial data of the areas of the faces and the areas of the medial parallelograms…
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new…
In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in arXiv:1506.03053. Our method is based on the relation…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian…
Let $A$ be the path algebra of a finite acyclic quiver $Q$ over a finite field. We realize the quantum cluster algebra with principal coefficients associated to $Q$ as a sub-quotient of a certain Hall algebra involving the category of…
In arXiv:0912.1346, four quantum dilogarithm identities containing infinitely many factors are proposed as wall-crossing formula for refined BPS invariant. We give algebraic proof of these identities using the formula for universal R-matrix…
We consider the $R$-matrix presentations of the quantum queer superalgebra $U_q(q_n)$ and its affine counterpart $U_q(\widehat q_n)$. We derive crossing symmetry relations for the $R$-matrices and use them to construct central elements in…
In this paper we study a functional equation associated to the Kummer's equation (K) of the trilogarithm. Then we apply our results to web geometry and to characterize the functions solution of (K).
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic…
This is a study of orbifold-quotients of quantum groups (quantum orbifolds $\Theta \rightrightarrows G_q$). These structures have been studied extensively in the case of the quantum $SU_2$ group. I will introduce a generalized mechanism…