459 research outputs found
The symmetries of the Dirac--Pauli equation in two and three dimensions
We calculate all symmetries of the Dirac-Pauli equation in two-dimensional
and three-dimensional Euclidean space. Further, we use our results for an
investigation of the issue of zero mode degeneracy. We construct explicitly a
class of multiple zero modes with their gauge potentials.Comment: 22 pages, Latex. Final version as published in JMP. Contains an
additional subsection (4.2) with the explicit construction of multiple zero
mode
Conservation laws in Skyrme-type models
The zero curvature representation of Zakharov and Shabat has been generalized
recently to higher dimensions and has been used to construct non-linear field
theories which either are integrable or contain integrable submodels. The
Skyrme model, for instance, contains an integrable subsector with infinitely
many conserved currents, and the simplest Skyrmion with baryon number one
belongs to this subsector. Here we use a related method, based on the geometry
of target space, to construct a whole class of theories which are either
integrable or contain integrable subsectors (where integrability means the
existence of infinitely many conservation laws). These models have
three-dimensional target space, like the Skyrme model, and their infinitely
many conserved currents turn out to be Noether currents of the
volume-preserving diffeomorphisms on target space. Specifically for the Skyrme
model, we find both a weak and a strong integrability condition, where the
conserved currents form a subset of the algebra of volume-preserving
diffeomorphisms in both cases, but this subset is a subalgebra only for the
weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106
correcte
A BPS Skyrme model and baryons at large Nc
Within the class of field theories with the field contents of the Skyrme
model, one submodel can be found which consists of the square of the baryon
current and a potential term only. For this submodel, a Bogomolny bound exists
and the static soliton solutions saturate this bound. Further, already on the
classical level, this BPS Skyrme model reproduces some features of the liquid
drop model of nuclei. Here, we investigate the model in more detail and,
besides, we perform the rigid rotor quantization of the simplest Skyrmion (the
nucleon). In addition, we discuss indications that the viability of the model
as a low energy effective field theory for QCD is further improved in the limit
of a large number of colors N_c.Comment: latex, 23 pages, 1 figure, a numerical error in section 3.2
corrected; matches published versio
Integrable theories in any dimension: a perspective
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of dimension by the introduction of a -form connection. The method has been used to study several theories of physical interest, like self-dual Yang-Mills theories, Bogomolny equations, non-linear sigma models and Skyrme-type models. The local version of the generalized zero curvature involves a Lie algebra and a representation of it, leading to a number of conservation laws equal to the dimension of that representation. We discuss the conditions a given theory has to satisfy in order for its associated zero curvature to admit an infinite dimensional (reducible) representation. We also present the theory in the more abstract setting of the space of loops, which gives a deeper understanding and a more simple formulation of integrability in any dimension
Investigation of restricted baby Skyrme models
A restriction of the baby Skyrme model consisting of the quartic and
potential terms only is investigated in detail for a wide range of potentials.
Further, its properties are compared with those of the corresponding full baby
Skyrme models. We find that topological (charge) as well as geometrical
(nucleus/shell shape) features of baby skyrmions are captured already by the
soliton solutions of the restricted model. Further, we find a coincidence
between the compact or non-compact nature of solitons in the restricted model,
on the one hand, and the existence or non-existence of multi-skyrmions in the
full baby Skyrme model, on the other hand.Comment: latex, 18 pages, 2 figures; some typos correcte
Investigation of the Nicole model
We study soliton solutions of the Nicole model - a non-linear
four-dimensional field theory consisting of the CP^1 Lagrangian density to the
non-integer power 3/2 - using an ansatz within toroidal coordinates, which is
indicated by the conformal symmetry of the static equations of motion. We
calculate the soliton energies numerically and find that they grow linearly
with the topological charge (Hopf index). Further we prove this behaviour to
hold exactly for the ansatz. On the other hand, for the full three-dimensional
system without symmetry reduction we prove a sub-linear upper bound,
analogously to the case of the Faddeev-Niemi model. It follows that symmetric
solitons cannot be true minimizers of the energy for sufficiently large Hopf
index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur
Estudio comparativo del blanqueo de la lana por los procedimientos de inmersión e impregnación-vaporizado.
El presente estudio ha tenido por objeto el conocimiento de la mejora del blanco experimentada por dos lanas de diferente coloración cuando se las somete a un blanqueo mixto continuo en una instalación piloto de tipo industrial, efectuando el blanqueo oxidante por el sistema de impregnación-vaporizado y el reductor en los compartimentos de la máquina destinados a tratamientos de lavado o posteriores. Los resultados obtenidos se han comparado con los que se derivan de la aplicación del blanqueo mixto discontinuo convencional, deduciéndose que el blanqueo mixto continuo proporciona blancos iguales o algo inferiores, según el grado de coloración de la lana inicial, degradaciones químicas inferiores, y evidentes ahorros en el consumo de productos, agua y energía térmica.This paper deals with the improvement of whiteness achieved by two kinds of wool, having different colouration, when they are submitted to a continuous and combined bleaching in an industrial pilot unit. The oxidizing bleaching is applied according to the pad-steam method and the reducing one takes place in the boxes of the machine provided for washing or post-treatments. The results found have been compared to the resulting ones from the application of a conventional noncontinuous and combined bleaching: the former provides similar or somewhat lower whiteness, according to the colouration degree of the initial wool, lower chemical degradation and an obvious economy in the consumption of water, heat power and chemicals.La présente étude a eu pour objet la connaissance de l'amélioration du blanc expérimentée par deux laines de différente coloration lorqu'on les soumet à un blanchissage mixte continu dans unes installation pilote industrielle en effectuant le blanchissage oxydant par le systeme imprégnation-vaporisage et celui réducteur dans les compartiments de la machine destinés a des traitements de lavage ou postérieurs. On a comparé les résultats obtenus avec ceux qui dérivent de l'application du blanchissage mixte discontinu conventionnel; on a pu en déduire que dans le blanchissage mixte continu les blancs sont égaux ou un peu inférieurs á ceux du blanchissage mixte discontinu, selon le degré de coloration de la laine initial, que les dégradations chimiques sont inférieures et que l'on réalise des économies évidentes de consommation de produits, d'eau et d'énergie thermique et électrique.Peer Reviewe
Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207
The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207),
propose an interesting method to solve the Faddeev model by reducing it to a
set of first order PDEs. They first construct a vectorial quantity , depending on the original field and its first derivatives, in terms of which
the field equations reduce to a linear first order equation. Then they find
vectors and which identically obey this linear
first order equation. The last step consists in the identification of the with the original as a function of the original field.
Unfortunately, the derivation of this last step in the paper cited above
contains an error which invalidates most of its results
Soliton stability in some knot soliton models
We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier
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