Related papers: Pieri rules, vertex operators and Baxter Q-matrix

Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…

An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results…

A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…

In this contribution, we give an integral representation of the wave functions of the quantum N-particle Toda chain with boundary interaction. In the case of the Toda chain with one-boundary interaction, we obtain the wave function by an…

Recursion relations for orthogonal polynominals, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equvalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro…

The quasiclassical solution to the extended Toda chain hierarchy, corresponding to the deformation of the simplest Seiberg-Witten theory by all descendants of the dual topological string model, is constructed explicitly in terms of the…

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance…

We consider the critical alternating quantum spin chain with ${q_{+}\over 2}$, ${q_{-} \over2}$ spins. Using the Bethe ansatz technique we find explicit expressions for the $S$-matrix of the model. We show that in the limit that $q_{\pm}…

Recently, a theoretical framework was set up in [1], which allows for the symmetry-preserving inclusion of full quark-gluon vertices in the description of the meson dynamics. In the present work, we develop a special truncation within this…

The integral representations for the eigenfunctions of $N$ particle quantum open and periodic Toda chains are constructed in the framework of Quantum Inverse Scattering Method (QISM). Both periodic and open $N$-particle solutions have…

We study the correlation between $\epe$ and $\Delta I=1/2$ rule in the framework of non-linear $\sigma$ model including scalar mesons. The matrix elements of QCD and Electroweak (EW) penguin operators are computed within factorization…

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that…

In this paper we propose algebraic universal procedure for deriving "fusion rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$ symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is got…

This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in…

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This…

We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…

For $q$ generic, Jimbo showed that $q$-tensor space $V_q^{\otimes r}$ (where $V_q$ is the $n$-dimensional vector representation) satisfies Schur--Weyl duality with respect to the commuting actions of the quantized enveloping algebra…

The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…