On the Stability of Randall-Sundrum Braneworlds with Conformal Bulk Fields

In the Randall-Sundrum scenario we consider exact 5-dimensional solutions with localized gravity which are associated with a well defined class of conformal bulk fields. We analyze their behaviour under radion field perturbations. We show that if the Randall-Sundrum exponential warp is the localizing metric function and the equation of state of the conformal fields is not changed by the radion perturbation then the 5-dimensional solutions are unstable. We present new stable solutions which describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytopic matter.Comment: 10 pages, latex, no figures. Contribution to the special issue of Vestnik of Tomsk State Pedagogical University in the field QFT/Cosmology/Gravity/Strings, edited by Sergei D. Odintso

Braneworlds, Conformal Fields and Dark Energy

In the Randall-Sundrum scenario we analize the dynamics of a spherically symmetric 3-brane when matter fields propagate in the bulk. For a well defined class of conformal fields of weight -4 we determine a new set of exact 5-dimensional solutions which localize gravity in the vicinity of the brane and are stable under radion field perturbations. Geometries which describe the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy are shown to belong to this set.Comment: 7 pages, latex, no figures. Talk given at the Fifth International Workshop on New Worlds in Astroparticle Physics, University of Algarve, Faro, 8-10 January 2005. To be published in the workshop proceeding

Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.Comment: 6 pages, LaTeX, 1 EPS figure. Talk given at the Workshop The Cosmology of Extra Dimensions and Varying Fundamental Constants of the Conference JENAM 2002, The Unsolved Universe: Challenges for the Future, 2-7 September 2002, Porto, Portuga

Implications of anomalous gauge boson interactions to the fermion electromagnetic moments

We calculate the electromagnetic fermion form-factors induced by the anomalous gauge boson interactions contained in the operators ODW and ODB. Other results regarding anomalous triple gauge boson interactions are briefly overviewed. We study the interplay between vertex corrections and gauge boson self-energies extended to the longitudinal degrees of freedom. The physical couplings to an external electromagnetic field are then derived.Comment: 14 pages, LATeX, to appear in Modern Physics Letters A, some literary changes, a few notation correction

Dark Radiation and Localization of Gravity on the Brane

We discuss the dynamics of a spherically symmetric dark radiation vaccum in the Randall-Sundrum brane world scenario. Under certain natural assumptions we show that the Einstein equations on the brane form a closed system. For a de Sitter brane we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We define the conditions leading to singular or globally regular solutions. We also analyse the localization of gravity near the brane and show that a phase transition to a regime where gravity propagates away from the brane may occur at short distances during the collapse of positive dark energy density.Comment: 7 pages, latex with 2 eps figures. Talk given by Rui Neves, Fourth International Workshop on New Worlds in Astroparticle Physics, Algarve University, Faro, 5-7 September, 2002. To be published in the corresponding proceedings, World Scientifi

Polchinski ERG equation and 2D scalar field theory

We investigate a $Z_2$-symmetric scalar field theory in two dimensions using the Polchinski exact renormalization group equation expanded to second order in the derivative expansion. We find preliminary evidence that the Polchinski equation is able to describe the non-perturbative infinite set of fixed points in the theory space, corresponding to the minimal unitary series of 2D conformal field theories. We compute the anomalous scaling dimension $\eta$ and the correlation length critical exponent $\nu$ showing that an accurate fit to conformal field theory selects particular regulating functions.Comment: 9 pages, latex with 2 figures, uses sprocl.sty. To be published in the Proceedings of the Workshop on the Exact Renormalization Group held in Faro, Portugal, in September 10-12 1998, World Scientifi

Polchinski ERG Equation in O(N) Scalar Field Theory

We investigate the Polchinski ERG equation for d-dimensional O(N) scalar field theory. In the context of the non-perturbative derivative expansion we find families of regular solutions and establish their relation with the physical fixed points of the theory. Special emphasis is given to the large N limit for which many properties can be studied analytically.Comment: 7 pages, 4 figures, uses latex sprocl style. Two references added. To be published in the proceedings of the Second Conference on the Exact Renormalization Group (Rome, September 18-22, 2000), World Scientifi

Braneworlds, Conformal Fields and the Gravitons

We investigate the dynamics of Randall-Sundrum AdS5 braneworlds with 5-dimensional conformal matter fields. In the scenario with a compact fifth dimension the class of conformal fields with weight -4 is associated with exact 5-dimensional warped geometries which are stable under radion field perturbations and describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy. We analyse the graviton mode flutuations around this class of background solutions and determine their mass eigenvalues and wavefunctions from a Sturm-Liouville problem. We show that the localization of gravity is not sharp enough for large mass hierarchies to be generated. We also discuss the physical bounds imposed by experiments in particle physics, in astrophysics and in precise measurements of the low energy gravitational interaction.Comment: LaTeX, 9 pages, 2 figures. Based on talk given in the Second International Conference on Quantum Theories and the Renormalization Group in Gravity and Cosmology, CSIC and University of Barcelona, Barcelona, Spain, 11-15 July 2006. Submitted to be published in the Conference Proceedings, J. Phys. A: Math. Ge

Da lógica do mosaico à lógica do projecto: as actividades de enriquecimento curricular na escola do 1º CEB

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A new path integral approximation to photon propagation in turbid media

The path integral approach is applied to describe the propagation of photons in bounded homogeneous turbid media. Introducing a new controlled perturbative expansion centred on the diffusion limit, new analytic solutions for continuous wave reflectance and transmittance are determined, as relevant for non-invasive measurements of tissue optical properties based on continuous wave photon migration instruments. A comparative analysis with the diffusion approximation of radiative transfer theory is made to show that non-diffusive effects are enhanced in turbid regions with increasing absorption coefficients and decreasing reduced scattering coefficients as well as when the distance between interface boundaries increases. The relation between the transport equation (which is the starting point for the path integral approach) and multiple scattering theory is also discussed