153 research outputs found

    Quantum and Classical Integrable Systems

    Full text link
    The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the universal enveloping algebra of an affine Lie algebra, or its q-deformation.) A similar relation also holds in the classical case. We discuss different guises of this very important relation and its implication for the description of the spectrum and the eigenfunctions of the quantum system. Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter School on Nonlinear Systems, Pondicherry, January 199

    The dual parametrization for gluon GPDs

    Full text link
    We consider the application of the dual parametrization for the case of gluon GPDs in the nucleon. This provides opportunities for the more flexible modeling unpolarized gluon GPDs in a nucleon which in particular contain the invaluable information on the fraction of nucleon spin carried by gluons. We perform the generalization of Abel transform tomography approach for the case of gluons. We also discuss the skewness effect in the framework of the dual parametrization. We strongly suggest to employ the fitting strategies based on the dual parametrization to extract the information on GPDs from the experimental data.Comment: 37 pages, 2 figure

    Sexually divergent expression of active and passive conditioned fear responses in rats

    Get PDF
    Traditional rodent models of Pavlovian fear conditioning assess the strength of learning by quantifying freezing responses. However, sole reliance on this measure includes the de facto assumption that any locomotor activity reflects an absence of fear. Consequently, alternative expressions of associative learning are rarely considered. Here we identify a novel, active fear response ('darting') that occurs primarily in female rats. In females, darting exhibits the characteristics of a learned fear behavior, appearing during the CS period as conditioning proceeds and disappearing from the CS period during extinction. This finding motivates a reinterpretation of rodent fear conditioning studies, particularly in females, and it suggests that conditioned fear behavior is more diverse than previously appreciated. Moreover, rats that darted during initial fear conditioning exhibited lower freezing during the second day of extinction testing, suggesting that females employ distinct and adaptive fear response strategies that improve long-term outcomes

    Hard Exclusive Pion Electroproduction at Backward Angles with CLAS

    Get PDF
    We report on the first measurement of cross sections for exclusive deeply virtual pion electroproduction off the proton, ep→e′nπ+, above the resonance region at backward pion center-of-mass angles. The φπ⁎-dependent cross sections were measured, from which we extracted three combinations of structure functions of the proton. Our results are compatible with calculations based on nucleon-to-pion transition distribution amplitudes (TDAs). These non-perturbative objects are defined as matrix elements of three-quark-light-cone-operators and characterize partonic correlations with a particular emphasis on baryon charge distribution inside a nucleon. Keywords: TDA, Exclusive single pion, Eletroproduction, CLA

    BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle

    Full text link
    The quantum double for the quantized BRST superalgebra is studied. The corresponding R-matrix is explicitly constucted. The Hopf algebras of the double form an analytical variety with coordinates described by the canonical deformation parameters. This provides the possibility to construct the nontrivial quantization of the proper time supergroup cotangent bundle. The group-like classical limit for this quantization corresponds to the generic super Lie bialgebra of the double.Comment: 11 pages, LaTe

    Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure

    Get PDF
    The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space sigma models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to symmetric space sine-Gordon models. This work therefore shows indirectly that symmetric space sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an integrable potential, have a mild non-ultralocality. The first step needed to construct an integrable discretization of these models is performed by determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change

    The sine-Gordon model with integrable defects revisited

    Get PDF
    Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

    G(2)-Calogero-Moser Lax operators from reduction

    Get PDF
    We construct a Lax operator for the G2G_2-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the A6A_6-model to a B3B_3-model with the help of an embedding of the B3B_3-root system into the A6A_6-root system together with the specification of certain coupling constants. The G2G_2-Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the G2G_2-system into the B3B_3-system. The degree of algebraically independent and non-vanishing charges is found to be equal to the degrees of the corresponding Lie algebra.Comment: 12 pages, Late

    Multiplicative slices, relativistic Toda and shifted quantum affine algebras

    Full text link
    We introduce the shifted quantum affine algebras. They map homomorphically into the quantized KK-theoretic Coulomb branches of 3d N=43d\ {\mathcal N}=4 SUSY quiver gauge theories. In type AA, they are endowed with a coproduct, and they act on the equivariant KK-theory of parabolic Laumon spaces. In type A1A_1, they are closely related to the open relativistic quantum Toda lattice of type AA.Comment: 125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 adde

    Gaudin Models and Bending Flows: a Geometrical Point of View

    Full text link
    In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym
    corecore