相关论文: 3-Cocycles and the Operator Product Expansion

We prove an operator level limit for the circular Jacobi $\beta$-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the…

We consider minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator.…

The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…

We describe the spectral properties of the Jacobi operator $(Hy)_n= a_{n-1} y_{n-1}+a_{n}y_{n+1}+b_ny_n,$ $n\in\Z,$ with $a_n=a_n^0+ u_n,$ $b_n= b_n^0+ v_n,$ where sequences $a_n^0>0,$ $b_n^0\in\R$ are periodic with period $q$, and…

The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy with…

The article studies a class of generalized factorial functions and symbolic product sequences through Jacobi type continued fractions (J-fractions) that formally enumerate the divergent ordinary generating functions of these sequences. The…

In this paper, we examine the problem of anomalies of the fermionic currents in the context of the very special relativity (VSR). We consider the VSR contributions to the triangle amplitude $\left\langle J_{5}^{\lambda} J^{\mu} J^{\nu}…

We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. $G_{\mu\nu}^a G^{a,\mu\nu}$, $m_i\bar q_j q_j$ and $m_i m_j m_k^2$, in the short-distance expansion of the time-ordered product of a…

We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kenser's criterion for Jacobi operators follows…

We prove the noncommutative analogue of Jacobi triple product identity. As an application we organizing the q-characters of circular quiver gauge theories into an infinite product. We conjecture the gauge origami theory interpretation of…

In this paper, we introduce and study non-local Jacobi operators, which generalize the classical (local) Jacobi operators. We show that these operators extend to generators of ergodic Markov semigroups with unique invariant probability…

Two-loop corrections for the <VVA> correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by…

We compute three-loop corrections to the singlet form factors for massive quarks using a semi-analytic method which provides precise results over the whole kinematic range. Particular emphasis is put on the anomaly contribution originating…

This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method. The analysis focuses on the outer or oscillatory region of…

There exist local infinitesimal redefinitions of the fermionic fields, which may be used to modify the strength of the coupling for the interaction term in massless QED3. Under those (formally unitary) transformations, the functional…

We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment problem is indeterminate. Our main goal is…

We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi…

We calculate within an algebraic Bjorken-Johnson-Low (BJL) method anomalous Schwinger terms of fermionic currents and the Gauss law operator in chiral gauge theories. The current algebra is known to violate the Jacobi identity in an…

Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average…

For Jacobi parameters belonging to one of the three classes: asymptotically periodic, periodically modulated and the blend of these two, we study the asymptotic behavior of the Christoffel functions and the scaling limits of the…