Bound on the Dark Matter Density in the Solar System from Planetary Motions

High precision planet orbital data extracted from direct observation, spacecraft explorations and laser ranging techniques enable to put a strong constraint on the maximal dark matter density of a spherical halo centered around the Sun. The maximal density at Earth's location is of the order $10^5$ ${\rm GeV/cm^3}$ and shows only a mild dependence on the slope of the halo profile, taken between 0 and -2. This bound is somewhat better than that obtained from the perihelion precession limits.Comment: 7 pages, 1 figur

Adventures in Nannydom: Reclaiming Collective Action for the Public's Health

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111158/1/jlme12221.pd

BF Actions for the Husain-Kuchar Model

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in Phys. Rev.

Bases in Lie and Quantum Algebras

Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su_q(2).Comment: 16 pages, Proceedings of the 5th International Symposium on Quantum Theory and Symmetries QTS5 (July 22-28, 2007, Valladolid (Spain)

An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications

We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series Z = \log(\e^X \e^Y) in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when $X$ and $Y$ are real or complex matrices.Comment: 30 page

Gaucher disease: A cause of massive splenomegaly in a 15-year-old black African male

Patients with Gaucher disease (GD), a rare autosomal recessive lysosomal storage disease, commonly present to paediatricians with massive splenomegaly. While the diagnosis and management of patients with this chronic multisystem disorder has evolved significantly in recent years, the initial diagnosis represents a challenge. We describe the case of a 15-year-old black African male who presented with abdominal distension, delayed growth and fatigue. Initial laboratory studies revealed severe anaemia (haemoglobin concentration 8 g/dL) and moderate thrombocytopenia (platelet count 80 × 109/L). A computed tomography scan of the abdomen showed an enlarged liver of 173 mm and massive splenomegaly of 27 mm. The diagnosis of GD was confirmed by reduced beta-glucocerebrosidase activity and heterozygous mutations in the GBA1 gene. The patient was managed at a dedicated paediatric haematology unit with enzyme replacement therapy and regular clinical, biochemical and radiological monitoring

Self-Dual Action for Fermionic Fields and Gravitation

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishing torsion. Thus, in the self-dual framework, the extra terms entering the equations of motion with respect to the standard Einstein-Dirac field equations, are neatly associated with torsion.Comment: 13 pages, plain-tex, recently appearing in Nuovo Cimento B, volume 109, pages 973-982, September 199