A K-Theoretic Proof of Boutet de Monvel's Index Theorem for Boundary Value Problems

We study the C*-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with non-empty boundary. We find short exact sequences in K-theory 0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact ideal and T*X' the cotangent bundle of the interior of X. Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show that the Fredholm index of an elliptic element in A is given as the composition of the topological index with mapping K_1(A/K)->K_0(C_0(T*X')) defined above. This relation was first established by Boutet de Monvel by different methods.Comment: Title slightly changed. Accepted for publication in Journal fuer die reine und angewandte Mathemati

C*-Structure and K-Theory of Boutet de Monvel's Algebra

We consider the norm closure $A$ of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold $X$ with boundary $Y$. We first describe the image and the kernel of the continuous extension of the boundary principal symbol to $A$. If the $X$ is connected and $Y$ is not empty, we then show that the K-groups of $A$ are topologically determined. In case the manifold, its boundary and the tangent space of the interior have torsion-free K-theory, we prove that $K_i(A/K)$ is isomorphic to the direct sum of $K_i(C(X))$ and $K_{1-i}(C_0(TX'))$, for i=0,1, with $K$ denoting the compact ideal and $TX'$ the tangent bundle of the interior of $X$. Using Boutet de Monvel's index theorem, we also prove this result for i=1 without assuming the torsion-free hypothesis. We also give a composition sequence for $A$.Comment: Final version, to appear in J. Reine Angew. Math. Improved K-theoretic result

Galactic Nonlinear Dynamic Model

We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance with the observational data.Comment: 6 pages, 1 figure. Talk given in the 7th Alexander Friedmann International Seminar, June 29 to July 5, 2008, Joao Pessoa, PB, Brazi

Light-front quark distributions in the nucleon and nucleon electromagnetic form factors

Longitudinal and transverse quark momentum distributions in the nucleon are calculated from a phenomenological quark-nucleon vertex function obtained through an investigation of the nucleon electromagnetic form factors within a light-front framework.Comment: 6 pages, 11 figs. proceedings of LC2009, to appear in Nucl. Phys.

Timelike and spacelike hadron form factors, Fock state components and light-front dynamics

A unified description of spacelike and timelike hadron form factors within a light-front model was successfully applied to the pion. The model is extended to the nucleon to study the role of $q \bar q$ pair production and of nonvalence components in the nucleon form factors. Preliminary results in the spacelike range $0 \le Q^2 \le 10 ~ (GeV/c)^2$ are presented.Comment: 4 pages, espcrc1.sty. proceedings of FB XVIII (August 2006, Brazil), to be published in Nucl. Phys.

Electromagnetic Hadron Form Factors and Higher Fock Components

Investigation of the spacelike and timelike electromagnetic form factors of hadrons, within a relativistic microscopical model characterized by a small set of hypothesis, could shed light on the components of hadron states beyond the valence one. Our relativistic approach has been successfully applied first to the pion and then the extension to the nucleon has been undertaken. The pion case is shortly reviewed as an illustrative example for introducing the main ingredients of our approach, and preliminary results for the nucleon in the spacelike range $-10 (GeV/c)^2\le q^2 \le 0$ are evaluated.Comment: 8 pages, 6 figs, espcrc1.sty included. Proceedings of Fifth International Conference on Perspectives In Hadronic Physics, ICTP, May 22-26, 200

Neutrino Masses and Absence of Flavor Changing Interactions in the 2HDM from Gauge Principles

We propose several Two Higgs Doublet Models with the addition of an Abelian gauge group which free the usual framework from flavor changing neutral interactions and explain neutrino masses through the seesaw mechanism. We discuss the kinetic and mass-mixing gripping phenomenology which encompass several constraints coming from atomic parity violation, the muon anomalous magnetic moment, rare meson decays, Higgs physics, LEP precision data, neutrino-electron scattering, low energy accelerators and LHC probes.Comment: 54 pages, 10 figure

Why pair production cures covariance in the light-front?

We show that the light-front vaccum is not trivial, and the Fock space for positive energy quanta solutions is not complete. As an example of this non triviality we have calculated the electromagnetic current for scalar bosons in the background field method were the covariance is restored through considering the complete Fock space of solutions. We also show thus that the method of "dislocating the integration pole" is nothing more than a particular case of this, so that such an "ad hoc" prescription can be dispensed altogether if we deal with the whole Fock space. In this work we construct the electromagnetic current operator for a system composed of two free bosons. The technique employed to deduce these operators is through the definition of global propagators in the light front when a background electromagnetic field acts on one of the particles.Comment: 11 pages, 2 figure

Electromagnetic form factors of the nucleon in spacelike and timelike regions

An approach for a unified description of the nucleon electromagnetic form factors in spacelike and timelike regions is presented. The main ingredients of our model are: $i)$ a Mandelstam formula for the matrix elements of the nucleon electromagnetic current; $ii)$ a 3-dimensional reduction of the problem on the Light-Front performed within the so-called {\tt Propagator Pole Approximation} ({\bf PPA}), which consists in disregarding the analytical structure of the Bethe-Salpeter amplitudes and of the quark-photon vertex function in the integration over the minus components of the quark momenta; $iii)$ a dressed photon vertex in the $q\bar{q}$ channel, where the photon is described by its spin-1, hadronic component.Comment: 8 pages, 9 figs., macro added. Proceedings of the XI Conf. on Problems in Theoretical Nuclear Physics, Cortona, Oct. 11-14, 200