相关论文: Spin Chains and Gustafson's Integrals

We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by…

We introduce a new family of integrable theories with $N$ bosons and $N$ freely adjustable mass parameters. These theories restrict in particular limits to the ``generalized supersymmetric'' sine-Gordon models, as well as to the flavor…

Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…

We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin…

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…

We present a short review of the spin curvatures that arise within the framework of one of the Infeld-van der Waerden formalisms for general relativity. All the spinor symmetries borne by the inner structure of general relativity are thus…

Generalized parton distributions are a new type of hadronic observables which has recently stimulated great interest among theorists and experimentalists alike. Introduced to delineate the spin structure of the nucleon, the orbital angular…

We study the general L_0-regular gl(2) spin chain, i.e. a chain where the sites {i,i+L_0,i+2L_0,...} carry the same arbitrary representation (spin) of gl(2). The basic example of such chain is obtained for L_0=2, where we recover the…

We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…

We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…

We present an alternative proof of Gustafson's generalization of the second Barnes' lemma.

Concise review of the basic properties of unitary matrix integrals. They are studied with the help of the three matrix models: the ordinary unitary model, Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model. Especial…

The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The suggested formalism allows to address some subtle issues which…

The objective of this paper is to derive a representation of symmetric G-martingales as stochastic integrals with respect to the G-Brownian motion. For this end, we first study some extensions of stochastic calculus with respect to…

In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…

We study multi-variable integrals, that we name Sklyanin-Whittaker integrals, and prove their determinantal formulas. We also discuss a $q$-deformation, a determinantal point process, and associated Mellin--Barnes integrals.

We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to…

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of Giant Gravitons in the AdS/CFT correspondence. We show how to quantize…

Five and six dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted $XXZ$ spin chain, while…