Related papers: State integral models and the tetrahedron equation
The Faddeev equations for the three-body bound state are solved directly as thre e-dimensional integral equations without employing partial wave decomposition. Two-body forces of the Malfliet-Tjon type and simple spin independent genuine…
A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables…
In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star-triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic…
We investigate the role of pressure in a class of generalised Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute…
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an…
We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The…
We define classes of quantum states associated to isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical pseudo-differential operators and covariant under the action of semiclassical Fourier…
The paper considers the geometry of the Modified Solid-Liquid-Vapour equation of state. This model describes a substance state in three phases. Thermodynamics states are points on Legendrian or Lagrangian manifolds in the corresponding…
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that arises as the linearization of the equation…
The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition…
We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge…
We introduce the notion of an isotropic quantum state associated with a Bohr-Sommerfeld manifold in the context of Berezin-Toeplitz quantization of general prequantized symplectic manifolds, and we study its semi-classical properties using…
We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative,…
We count the Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel…
This paper represents a continuation of our previous work, where the Bolzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus…
The ab-initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of…
We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated…
It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…