Related papers: Reflection Bootstrap Equations for Toda Field Theo…
We propose explicit expressions for the boundary reflection matrices of the ${\cal A}_m+(r,s)$ series of massive scattering theories, obtained by perturbing the ${\cal A}_m$ unitary minimal models with $(r,s)$ boundary conditions with both…
We have find the diagonal K matrix solutions of the reflection equations for a class of vertex models. These models have (n+1)(2n+1) vertices and are defined as two set of (n + 1) R matrices, solutions of the equations of Yang-Baxter…
The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is…
We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS…
The first part of this work consists of a study of the ODE/IM correspondence for simply-laced affine Toda field theories. It is a first step towards a full generalisation of the results of Lukyanov and Zamolodchikov on $\hat{\mathfrak a}_1$…
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
This thesis concerns the algebraic consequences of Freyd's Generating Hypothesis, and explores the question of whether there exists a self-injective ring R that can be constructed purely algebraically that exhibits some of the known…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the graded version of the $A_{n-1}^{(1)}$ affine Lie algebra, the $U_{q}[sl(m|n)^{(1)}]$ vertex model, also known as…
Recently, researchers have proposed the Asymmetric Bethe ansatz method - a theoretical tool that extends the scope of Bethe ansatz-solvable models by "breaking" partial mirror symmetry via the introduction of a fully reflecting boundary.…
We quantize $sl_n$ Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the case of the defining representation. In the $sl_3$ case we extend the analysis also to…
The purpose of this talk is to sketch some recent progress which has been made in calculating non-perturbatively the reflection factors for the sinh-Gordon model restricted to a half-line by integrable boundary conditions. The essential…
We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity…
Affine quantum groups are certain pseudo-quasitriangular Hopf algebras that arise in mathematical physics in the context of integrable quantum field theory, integrable quantum spin chains, and solvable lattice models. They provide the…
The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been…
We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a…
We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation…
Reflection equation algebras and related U_q(g)-comodule algebras appear in various constructions of quantum homogeneous spaces and can be obtained via transmutation or equivalently via twisting by a cocycle. In this paper we investigate…
It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $C_{n}^{(1)}$, $D_{n}^{(1)}$ and $A_{2n-1}^{(2)}$ affine Lie algebras. We find three types of solutions with $n$,…
A cross between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system, is introduced for any affine root system. Though it is not completely integrable but partially integrable, or quasi exactly…