Related papers: Open Spin Chains and Quadratic Algebras
An algebraic analysis framework for quantum calculus is proposed. The quantum derivative operator $D_{\tau ,\sigma}$ is based on two commuting bijections $\tau$ and $\sigma$ defined on an arbitrary set $M$ equipped with a tension structure…
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m\geq2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant graphs.
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
We derive a class of cubic interaction vertices for three higher spin fields, with integer spins $\lambda_1$, $\lambda_2$, $\lambda_3$, by closing commutators of the Poincar\'e algebra in four-dimensional flat spacetime. We find that these…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…
We study the holomorphic twist of 3d ${\cal N}=2$ gauge theories in the presence of boundaries, and the algebraic structure of bulk and boundary local operators. In the holomorphic twist, both bulk and boundary local operators form chiral…
The algebraic path problem provides a general setting for shortest path algorithms in optimization and computer science. This work extends the algebraic path problem to networks equipped with input and output boundaries. We show that the…
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable coefficient domain with a bialgebra structure, this…
We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the…
We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain…
We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of…