Related papers: Spin Chains and Gustafson's Integrals
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…
Mustafin varieties are flat degenerations of projective spaces, induced by a choice of an $n-$tuple of lattices in a vector space over a non-archimedean field. They were introduced by Mustafin in the 70s in order to generalise Mumford's…
We give an elementary proof of the Bazhanov-Reshetikhin determinant formula for rational transfer matrices of the twisted quantum super-spin chains associated with the gl(K|M) algebra. This formula describes the most general fusion of…
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…
We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…
We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
In these notes we generalize the theory of graphical functions from scalar theories to theories with spin.
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
Classical splines feature prominently in approximation theory and numerical analysis, while GKM theory arises in the study of equivariant cohomology. More recently, generalized splines have been studied which simultaneously generalize both…
We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number $s$. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that…
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
The dual parametrization and the Mellin-Barnes integral approach represent two frameworks for handling the double partial wave expansion of generalized parton distributions (GPDs) in the conformal partial waves and in the $t$-channel ${\rm…
We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as solutions of partial differential equations and we show that the generic p-spin…
In Quantum Field Theory, scattering amplitudes are computed from propagators which, for internal lines, are built upon spin/polarization-sum relationships. In turn, these are normally constructed upon plane-wave solutions of the free field…
We propose a definition of Mellin amplitudes for conformal correlators involving arbitrary spinning operators in tensor representations of the Lorentz group. These representations cover all bosonic local operators. Our strategy is to…
We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the…
It is shown, that the requirement of invariance under spatial rotations reveales an intrinsic fractional extended translation-rotation-like property for particles described with the fractional Schroedinger equation, which we call fractional…