GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.

Pair term in the electromagnetic current within the Front-Form dynamics: spin-0 case

The frame and scale dependence of the pair-term contribution to the electromagnetic form factor of a spin-zero composite system of two-fermions is studied within the Light Front. The form factor is evaluated from the plus-component of the current in the Breit frame, using for the first time a nonconstant, symmetric ansatz for the Bethe-Salpeter amplitude. The frame dependence is analyzed by allowing a nonvanishing plus component of the momentum transfer, while the dynamical scale is set by the masses of the constituents and by mass and size of the composite system. A transverse momentum distribution, associated with the Bethe-Salpeter amplitude, is introduced which allows to define strongly and weakly relativistic systems. In particular, for strongly relativistic systems, the pair term vanishes for the Drell-Yan condition, while is dominant for momentum transfer along the light-front direction. For a weakly relativistic system, fitted to the deuteron scale, the pair term is negligible up to momentum transfers of 1 (GeV/c)(2). A comparison with results obtained within the Front-Form Hamiltonian dynamics with a fixed number of constituents is also presented. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Spacetime algebraic skeleton

The cosmological constant is shown to have an algebraic meaning: it is essentially an eigenvalue of a Casimir invariant of the Lorentz group acting on the spaces tangent to every spacetime. This is found in the context of de Sitter spacetimes, for which the Einstein equation is a relation between operators. Nevertheless, the result brings, to the foreground the skeleton algebraic structure underlying the geometry of general physical spacetimes. which differ from one another by the fleshening of that structure by different tetrad fields.

Solitons from dressing in an algebraic approach to the constrained KP hierarchy

The algebraic matrix hierarchy approach based on affine Lie sl(n) algebras leads to a variety of 1 + 1 soliton equations. By varying the rank of the underlying sl(n) algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarchy.The soliton solutions are then obtained as elements of the orbits of the dressing transformations constructed in terms of representations of the vertex operators of the affine sl(n) algebras realized in the unconventional gradations. Such soliton solutions exhibit non-trivial dependence on the KdV (odd) time flows and KP (odd and even) time Bows which distinguishes them From the conventional structure of the Darboux-Backlund-Wronskian solutions of the constrained KP hierarchy.

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

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

Light composite Higgs boson from the normalized Bethe-Salpeter equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Frame dependence of the pair contribution to the pion electromagnetic form factor in a light-front approach

The frame dependence of the pair-term contribution to the electromagnetic form factor of the pion is studied within the Light Front approach. A symmetric ansatz for the pion Bethe-Salpeter amplitude with a pseudo scalar coupling of the constituent to the pion field is used. In this model, the pair term vanishes for the Drell-Yan condition, while it is dominant for momentum transfer along the light-front direction.

A aproximação de campo médio de Bethe-Peierls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)