O modelo de Skyrme-Faddeev para o SU(N)

Pós-graduação em Física - IFT

Euclidean 4d exact solitons in a Skyrme type model

We introduce a Skyrme type, four-dimensional Euclidean field theory made of a triplet of scalar fields n→, taking values on the sphere S2, and an additional real scalar field φ, which is dynamical only on a three-dimensional surface embedded in R4. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory. © 2004 Elsevier B.V. All rights reserved.

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Construção exata de sólitons de Hopf

Pós-graduação em Física - IFT

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Infrared dynamics in (2+1) dimensions

In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the Kulish-Faddeev model for QED (quantum electrodynamics) in four space-time dimensions.

Infinite symmetries in the Skyrme model

We show that the Skyrme theory possesses a submodel with an infinite number of local conserved currents. The constraints leading to the submodel explore a decomposition of SU(2) with a complex field parametrizing the symmetric space SU(2)/U(1) and a real field in the direction of U(1). We demonstrate that the Skyrmions of topological charges ii belong to such integrable sector of the theory. Our results open ways to the development of exact methods, compensating for the non-existence of a BPS type sector in the Skyrme theory. (C) 2001 Published by Elsevier B.V. B.V.

The Faddeev-Jackiw approach and the conformal affine sl(2) Toda model coupled to the matter field

The conformal affine sl(2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry. (C) 2000 Academic Press.

The SU(2) Skyrme model and anomaly

The SU(2) Shyrme model, expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. in this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure. (C) 2000 Elsevier B.V. B.V. All rights reserved.

STRONG COUPLING LIMITS and QUANTUM ISOMORPHISMS of THE GAUGED THIRRING MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models

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

Ground state masses and binding energies of the nucleon, hyperon and heavy baryons in a light-front model

The ground state masses and binding energies of the nucleon, lambda0, lambdac+ , lambdab0 are studied within a constituent quark QCD-inspired light-front model. The light-front Faddeev equations for the Qqq composite spin 1/2 baryons, are derived and solved numerically. The experimental data for the masses are qualitatively described by a flavor independent effective interaction.

Coordinate-space Faddeev-Hahn-type approach to three-body charge-transfer reactions involving exotic particles

Low-energy muon-transfer cross sections and rates in collisions of muonic atoms with hydrogen isotopes are calculated using a six-state close-coupling approximation to coordinate-space Faddeev-Hahn-type equations. In the muonic case satisfactory results are obtained for all hydrogen isotopes and the experimentaly observed strong isotopic dependence of transfer rates is also reproduced. A comparison with results of other theoretical and available experimental works is presented. The present model also leads to good transfer cross sections in the well-understood problem of antihydrogen formation in antiproton-positronium collision.

Nonpertubative solutions of massless gauged thirring model

We present a nonperturbative quantization of the two-dimensional massless gauged Thirring model by using the path-integral approach. First, we will study the constraint structure of model via the Dirac's formalism and by using the Faddeev-Senjanovic method we calculate the vacuum-vacuum transition amplitude in a Rξ-gauge, then we compute the Green's functions in a nonperturbative framework. © 2010 American Institute of Physics.

Relativistic three-body model for final state interaction in D+ → K-π+π+ decay

A challenge in mesonic three-body decays of heavy mesons is to quantify the contribution of re-scattering between the final mesons. D decays have the unique feature that make them a key to light meson spectroscopy, in particular to access the Kn S-wave phase-shifts. We built a relativis-tic three-body model for the final state interaction in D+ → K -π+π+ decay based on the ladder approximation of the Bethe-Salpeter equation projected on the light-front. The decay amplitude is separated in a smooth term, given by the direct partonic decay amplitude, and a three-body fully interacting contribution, that is factorized in the standard two-meson resonant amplitude times a reduced complex amplitude that carries the effect of the three-body rescattering mechanism. The off-shell reduced amplitude is a solution of an inhomogeneous Faddeev type three-dimensional integral equation, that includes only isospin 1/2 K -π+ interaction in the S-wave channel. The elastic K-π+ scattering amplitude is parameterized according to the LASS data[1]. The integral equation is solved numerically and preliminary results are presented and compared to the experimental data from the E791 Collaboration[2, 3] and FOCUS Collaboration[4, 5].