Bootstrap Equations for String-Like Amplitude

One of the ways to check the consistency of our effective field theory (EFT) approach (explained by A.Vereshagin and V.Vereshagin at this conference) is to perform the numerical testing of those sum rules for hadron resonance parameters which follow from the system of bootstrap constrains. In this talk we discuss the peculiar features of this procedure for the case of exactly solvable bootstrap model based on Veneziano string amplitude. This allows us to simulate different situations that may encounter in realistic EFT models. We also make a short review of the technique that may be useful for further analysis of various bootstrap systems.Comment: 7 pages, talk given at QFTHEP 2004, Russia, June 2004, to be published in Proceeding

Towards Drinfeld-Sokolov reduction for quantum groups

In this paper we study the Poisson-Lie version of the Drinfeld-Sokolov reduction defined in q-alg/9704011, q-alg/9702016. Using the bialgebra structure related to the new Drinfeld realization of affine quantum groups we describe reduction in terms of constraints. This realization of reduction admits direct quantization. As a byproduct we obtain an explicit expression for the symplectic form associated to the twisted Heisenberg double and calculate the moment map for the twisted dressing action. For some class of infinite-dimensional Poisson Lie groups we also prove an analogue of the Ginzburg-Weinstein isomorphism.Comment: 30 pages, LaTeX 2

Integrable Systems and Factorization Problems

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is to explain how the factorization problems (typically, the matrix Riemann problem) generate the entire small world of Integrable Systems along with the geometry of the phase space, Hamiltonian structure, Lax representations, integrals of motion and explicit solutions. The key tool will be the \emph{% classical r-matrix} (an object whose other guise is the well-known Hilbert transform). I do not give technical details, unless they may be exposed in a few lines; on the other hand, all motivations are given in full scale whenever possible.Comment: LaTeX 2.09, 69 pages. Introductory lectures on Integrable systems, Classical r-matrices and Factorization problem

On the equivalence of GPD representations

Phenomenological representations of generalized parton distributions (GPDs) implementing the non-trivial field theoretical requirements are employed in the present day strategies for extracting of hadron structure information encoded in GPDs from the observables of hard exclusive reactions. Showing out the equivalence of various GPD representations can help to get more insight into GPD properties and allow to build up flexible GPD models capable of satisfactory description of the whole set of available experimental data. We review the mathematical aspects of establishing equivalence between the the double partial wave expansion of GPDs in the conformal partial waves and in the $t$-channel ${\rm SO}(3)$ partial waves and the double distribution representation of GPDs.Comment: A contribution into the Proceedings of QUARKS-2016 19th International Seminar on High Energy Physics, Pushkin, Russia, 29 May - 4 June, 201

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