22,993 research outputs found
T-Duality in 2-D Integrable Models
The non-conformal analog of abelian T-duality transformations relating pairs
of axial and vector integrable models from the non abelian affine Toda family
is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear
in J. Phys.
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
A higher grading affine algebraic construction of integrable hierarchies,
containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is
proposed. We show that a two-component generalization of the Sch\" afer-Wayne
short pulse equation arises quite naturally from the first negative flow of the
WKI hierarchy. Some novel integrable nonautonomous models are also proposed.
The conserved charges, both local and nonlocal, are obtained from the Riccati
form of the spectral problem. The loop-soliton solutions of the WKI hierarchy
are systematically constructed through gauge followed by reciprocal B\" acklund
transformation, establishing the precise connection between the whole WKI and
AKNS hierarchies. The connection between the short pulse equation with the
sine-Gordon model is extended to a correspondence between the two-component
short pulse equation and the Lund-Regge model
The algebraic structure behind the derivative nonlinear Schroedinger equation
The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\"
odinger equation (DNLSE) amongst others interesting and important nonlinear
integrable equations. In this paper, a general higher grading affine algebraic
construction of integrable hierarchies is proposed and the KN hierarchy is
established in terms of a Kac-Moody algebra and principal
gradation. In this form, our spectral problem is linear in the spectral
parameter. The positive and negative flows are derived, showing that some
interesting physical models arise from the same algebraic structure. For
instance, the DNLSE is obtained as the second positive, while the Mikhailov
model as the first negative flows, respectively. The equivalence between the
latter and the massive Thirring model is explicitly demonstrated also. The
algebraic dressing method is employed to construct soliton solutions in a
systematic manner for all members of the hierarchy. Finally, the equivalence of
the spectral problem introduced in this paper with the usual one, which is
quadratic in the spectral parameter, is achieved by setting a particular
automorphism of the affine algebra, which maps the homogeneous into principal
gradation.Comment: references adde
Axial Vector Duality in Affine NA Toda Models
A general and systematic construction of Non Abelian affine Toda models and
its symmetries is proposed in terms of its underlying Lie algebraic structure.
It is also shown that such class of two dimensional integrable models naturally
leads to the construction of a pair of actions related by T-duality
transformationsComment: 9 pages, to appear in JHEP Proc. of the Workshop on Integrable
Theories, Solitons and Duality, IFT-Unesp, Sao Paulo, Brasil, one reference
adde
Noncommutativity due to spin
Using the Berezin-Marinov pseudoclassical formulation of spin particle we
propose a classical model of spin noncommutativity. In the nonrelativistic
case, the Poisson brackets between the coordinates are proportional to the spin
angular momentum. The quantization of the model leads to the noncommutativity
with mixed spacial and spin degrees of freedom. A modified Pauli equation,
describing a spin half particle in an external e.m. field is obtained. We show
that nonlocality caused by the spin noncommutativity depends on the spin of the
particle; for spin zero, nonlocality does not appear, for spin half, , etc. In the relativistic case the noncommutative
Dirac equation was derived. For that we introduce a new star product. The
advantage of our model is that in spite of the presence of noncommutativity and
nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation
it gives noncommutativity with a nilpotent parameter.Comment: 11 pages, references adda
T-Duality in Affine NA Toda Models
The construction of Non Abelian affine Toda models is discussed in terms of
its underlying Lie algebraic structure. It is shown that a subclass of such non
conformal two dimensional integrable models naturally leads to the construction
of a pair of actions which share the same spectra and are related by canonical
transformations.Comment: 6 pages, Presented at the 13th International Colloquium on Integrable
Systems and Quantum Groups, Prague, June, 200
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