Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

Mass generation from Lie algebra extensions

Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg-Salam theory are present, and a few others which are nevertheless consistent within the model.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

Discretizing the deformation parameter in the su(q)(2) quantum algebra

Inspired in recent works of Biedenham [1, 2] on the realization of the q-algebra su(q)(2), We show in this note that the condition [2j + 1](q) = N-q(j) = integer, implies the discretization of the deformation parameter alpha, where q = e(alpha). This discretization replaces the continuum associated to ct by an infinite sequence alpha(1), alpha(2), alpha(3),..., obtained for the values of j, which label the irreps of su(q)(2). The algebraic properties of N-q(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of alpha.

Low dimensional behavior in three-dimensional coupled map lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent 1 is observed. (C) 2011 Elsevier B.V. All rights reserved.

The non-twist standard map with robust tori

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Labyrinthic standard non-twist map

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the number of singularities in generic deformations of map germs

Let f:C-n, 0 --> C-p, 0 be a K-finite map germ, and let i = (i(1),..., i(k)) be a Boardman symbol such that Sigma(i) has codimension n in the corresponding jet space J(k)(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of Sigma(i) points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n - i(1) and, in addition, in the case p = 6, f must be a singularity of type Sigma(i2.i2).

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Genetic linkage map of chicken chromosome 1 from a Brazilian resource population

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CURRENT-ALGEBRA OF SUPER WZNW MODELS

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super-affine Lie algebras as expected, but, in general, them are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields; the purely fermionic sector displays an affine Lie algebra as well.

Non-Abelian Sugawara construction and the q-deformed N=2 superconformal algebra

The construction of a q-deformed N = 2 superconformal algebra is proposed in terms of level-1 currents of the U-q(<(su)over cap>(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed energy-momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to U-q(<(su)over cap>(N + 1)) is also proposed.