153 research outputs found
Quantum and Classical Integrable Systems
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
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
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
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
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
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
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
We construct a Lax operator for the -Calogero-Moser model by means of a
double reduction procedure. In the first reduction step we reduce the
-model to a -model with the help of an embedding of the -root
system into the -root system together with the specification of certain
coupling constants. The -Lax operator is obtained thereafter by means of
an additional reduction by exploiting the embedding of the -system into
the -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
We introduce the shifted quantum affine algebras. They map homomorphically
into the quantized -theoretic Coulomb branches of SUSY
quiver gauge theories. In type , they are endowed with a coproduct, and they
act on the equivariant -theory of parabolic Laumon spaces. In type ,
they are closely related to the open relativistic quantum Toda lattice of type
.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
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
- …