Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity

The conserved charges associated to gauge symmetries are defined at a boundary component of space-time because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined through integration by parts whereas each component of the boundary should be considered separately. We treat the example of gravity (for any space-time dimension, with or without cosmological constant), formulated as an Affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first order formulations. We then show that the superpotential associated to a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or AdS spacetimes) is the one proposed by Katz, Bi\u{c}{\'a}k and Lynden-Bell and not that of Komar. We finally discuss the KBL superpotential at null infinity.Comment: 16 pages, minor corrections and references added. Final version to appear in CQ

Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity

E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. This is an example of a new and general Forcing Rule.Comment: 64 pages, LaTeX. Version 2 has two more references and one misprint corrected. Accepted in Classical and Quantum Gravit

Antigen, antibody and immune complex detection in serum samples from rats experimentally infected with Strongyloides venezuelensis

AbstractIn order to establish an antigen, antibody and immune complex detection by enzyme-linked immunosorbent assay (ELISA) in serum samples, normal or immunocompromised Wistar rats experimentally infected with Strongyloides venezuelensis were used. The microtitre plates were coated with IgG anti-S. venezuelensis for antigen and immune complex detection and with alkaline parasite extract for antibody detection. Analysis revealed at least 12.5μg/mL of S. venezuelensis specific antigens in serum samples. Assay for antigen detection was not a good approach for evaluating infection in normal or immunocompromised rats. In normal rats IgG specific for S. venezuelensis was preferentially detected during the first 13days post-infection (p.i.) and immune complex detection was significantly reduced in 21 p.i. day. On the other hand, in immunocompromised rats, IgG and immune complex were detected during the entire kinetic (5, 8, 13 and 21 p.i). These results suggest that immune complex screening seems to be an alternative for early strongyloidiasis diagnosis in immunocompromised individuals

Anticorpos IgG anti-metacestódeo de Taenia solium em amostras de soro de habitantes da região centro-oeste do Brasil

A total of 354 serum samples from inhabitants who frequent the Clinical Laboratory in Catalão, Goiás, in the central-western region of Brazil, were collected from June to August, 2002. The samples were evaluated by indirect immunofluorescence antibody tests and an enzyme linked immunosorbent assay in order to detect anti-Taenia solium metacestode IgG antibodies. Reactive and inconclusive samples were tested by Western blotting (WB). Considering WB as a confirmation, the frequency of antibodies in the serum samples of the above population was 11.3% (CI 5.09 - 17.51). The immunodominant bands most frequently recognized in WB were 64-68 kDa (97.5%) and 47-52 kDa (80%). The percentage of seropositivity to cysticercosis was significantly higher for individuals residing in areas without sewage systems (p < 0.0001). In conclusion, the results indicate a probable endemic situation of cysticercosis in this population. These results reinforce the urgent need for control and prevention measures to be taken by the local public health services.Um total de 354 amostras de soro de habitantes que freqüentaram o Laboratório Clínico em Catalão, Goiás, na região centro-oeste do Brasil, foram colhidas no período de junho a agosto de 2002. As amostras foram avaliadas pelo teste de imunofluorescência indireta e enzyme-linked immunosorbent assay (ELISA) com o objetivo de detectar anticorpos IgG anti-metacestódeo de Taenia solium. As amostras reativas e inconclusivas foram testadas pelo Western blotting (WB). Considerando WB como reação confirmatória, a freqüência de anticorpos nas amostras de soro da população estudada foi 11,3% (IC: 5,09 - 17,51). As bandas imunodominantes mais frequentemente reconhecidas no WB foram 64-68 kDa (97,5%) e 47-52 kDa (80%). A porcentagem de soropositividade para cisticercose foi significativamente maior nos indivíduos que residiam em áreas sem sistema de esgoto (p < 0,0001). Concluiu-se que os resultados indicam uma provável situação de endemicidade para cisticercose nesta população, reforçando a urgente necessidade de medidas de controle e prevenção que devem ser implantadas pelo serviço de saúde pública local

On Superpotentials and Charge Algebras of Gauge Theories

We propose a new "Hamiltonian inspired" covariant formula to define (without harmful ambiguities) the superpotential and the physical charges associated to a gauge symmetry. The criterion requires the variation of the Noether current not to contain any derivative terms in \partial_{\mu}\delta \f. The examples of Yang-Mills (in its first order formulation) and 3-dimensional Chern-Simons theories are revisited and the corresponding charge algebras (with their central extensions in the Chern-Simons case) are computed in a straightforward way. We then generalize the previous results to any (2n+1)-dimensional non-abelian Chern-Simons theory for a particular choice of boundary conditions. We compute explicitly the superpotential associated to the non-abelian gauge symmetry which is nothing but the Chern-Simons Lagrangian in (2n-1) dimensions. The corresponding charge algebra is also computed. However, no associated central charge is found for $n \geq 2$. Finally, we treat the abelian p-form Chern-Simons theory in a similar way.Comment: 32 pages, LaTex. The proposal is restricted to first order theories. An appendix is added. Some references are adde

Propuestas alternativas de determinación de precios: MPH vs. RNA

En los últimos años han proliferado los estudios sobre valoración y evolución del precio de los inmuebles debido a la conjunción de una serie de factores que han dado lugar a que los precios de la vivienda en propiedad en España hayan experimentado un crecimiento espectacular desde la década de los 80. La obtención de un mecanismo objetivo de valoración inmobiliaria resulta de interés para numerosos colectivos, entre los que cabe citar los propietarios, constructores, agentes de la propiedad inmobiliaria, inversores, entidades tasadoras, financieras, aseguradoras o la propia Administración. La vivienda como mercancía es un bien económico peculiar con una serie de características especiales que la diferencian del resto de bienes intercambiados que dan lugar a que existan determinantes de demanda y condiciones de oferta específicas de este mercado. Entre los factores que provocan y agudizan estas diferencias destacan la heterogeneidad, inmovilidad, indivisibilidad o durabilidad de la misma. La finalidad del presente estudio es modelizar el valor de transacción de la vivienda libre y multifamiliar (tipo piso) situada en la ciudad de Córdoba en zonas urbanas, es decir, a partir de una serie de atributos referentes al inmueble se tratará de proporcionar de una forma objetiva cuál es su precio de mercado. Para la obtención de los datos de trabajo se recurre a Agencias de la Propiedad Inmobiliaria (APIs) situadas en la capital cordobesa. La información suministrada refleja transacciones reales, por tanto el precio suministrado recoge el verdadero precio de mercado. La base de datos contiene un total de 2.888 registros correspondientes a pisos de venta libre vendidos a lo largo del primer semestre de 2006 y en la misma se recogen, además del precio de venta, una serie de características -tanto internas del inmueble, como externas del edificio donde éste se ubica-. Por otra parte, dentro de las variables que caracterizan a una vivienda también puede distinguirse entre: las numéricas o cuantitativas y las no numéricas o cualitativas. Estas últimas fueron tratadas por medio de índices que recogen a la vez varias características con el objetivo de poder atribuirles una interpretación cuantitativa. Para la determinación del precio final de transacción del inmueble se utilizan separadamente dos metodologías: la Metodología de Precios Hedónicos (MPH) y las Redes Neuronales Artificiales (RNA), efectuando finalmente una comparación entre el poder de predicción de ambas técnicas para terminar sugiriendo cuál es más apropiada para la valoración de una vivienda. La MPH analiza el precio del bien vivienda en función de sus principales características, considerando que la unidad de vivienda es conceptualizada no como bien homogéneo e indivisible, sino como una cesta de atributos individuales cada uno de los cuales contribuye a la provisión de uno o más servicios de vivienda. Por su parte, las Redes Neuronales Artificiales tienen un funcionamiento análogo al del cerebro humano y tratan de superar la inflexibilidad y linealidad de los modelos hedónicos tradicionales. La comparativa de ambas metodologías pone en evidencia que la RNA presenta un mayor poder de predicción que las estimaciones obtenidas a través de MPH.Several studies oriented to the estimation of prices in real estate markets have been published in the last decade, as properties values have sharply increased in Spain since the eighties. There are several potential users in need of an objective tool to estimate the price of dwellings: owners of houses and flats, builders, property agents, investment societies, insurance companies, or the public sector department as the fiscal or municipal authorities. Real estate properties are a peculiar economic good that makes them different from the rest. The market for dwellings has some specific characteristics that originate its own offer and demand functions, such as their singularity and heterogeneity; they are non movable and indivisible, and are associated with long term investments. In this paper, the modelling of property value has been developed with a sample of sales in the city of Cordoba, that is, in an urban zone. From a series of attributes relating to the housing it will try to provide of an objective form which is the price of market. Some exogenous variables are considered, related to the property, the building and its environment. The market price has been recorded for 2888 sales during the first semester of 2006; these have been provided by the Real Estate Agencies involved in the study. Categorical data have been summarized through some ad hoc functions that estimate the importance of several related characteristics of each unit. In paragraph empirical it comes to determining the price of housing in Cordoba using two methods: Pricing Methodology Hedonics (PMH) and Artificial Neural Networks (ANN). PMH analyzes housing prices depending on their main characteristics, considering that the unit of housing is conceptualized not as homogeneous and indivisible good, but as a basket of individual attributes each of which contributes to the provision of one or more services of housing. ANN has an analogous functioning to that of the human brain. The hedonic and the neural networks models have been specified with the same exogenous variables and training data set, to be able to compare their relative forecasting power. In both approaches, a dwelling is composed by non separable attributes that should be valued separately. Neural networks models provide a more flexible tool that can adapt better than hedonic models to nonlinearities of the real estate markets, and with larger forecasting power

Brane-World charges

As opposed to usual Einstein gravity in four dimensions, the Brane-World scenario allows the construction of a local density of gravitational energy (and also of momentum, of angular momentum, etc...). This is a direct consequence of the hypothesis that our universe is located at the boundary of a five-dimensional diffeomorphism invariant manifold. We compute these Brane-World densities of charge using the Lanczos-Israel boundary conditions. To proceed, we implement an explicitely covariant generalization of the Hamiltonian procedure of Regge and Teitelboim given in a previous work. We finally study two simple Brane-World examples.Comment: 22 pages, LaTex. Minor errors corrected and references added. Final version to appear in Class. Qu. Gra

Black hole entropy and thermodynamics from symmetries

Given a boundary of spacetime preserved by a Diff(S^{1}) sub-algebra, we propose a systematic method to compute the zero mode and the central extension of the associated Virasoro algebra of charges. Using these values in the Cardy formula, we may derive an associated statistical entropy to be compared with the Bekenstein-Hawking result. To illustrate our method, we study in detail the BTZ and the rotating Kerr-adS_{4} black holes (at spatial infinity and on the horizon). In both cases, we are able to reproduce the area law with the correct factor of 1/4 for the entropy. We also recover within our framework the first law of black hole thermodynamics. We compare our results with the analogous derivations proposed by Carlip and others. Although similar, our method differs in the computation of the zero mode. In particular, the normalization of the ground state is automatically fixed by our construction.Comment: LaTeX, 23 pages, no figure

A Note on Conserved Charges of Asymptotically Flat and Anti-de Sitter Spaces in Arbitrary Dimensions

The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of both asymptotically flat and asymptotically AdS spacetimes in any dimension D bigger or equal to 4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions.The asymptotic symmetry algebra is found to be isomorphic either to the Poincare algebra or to the so(D-1, 2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly computed for Kerr and Kerr-AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments.Comment: 27 pages; v2 : references added, minor corrections; v3 : replaced to match published version forthcoming in General Relativity and Gravitatio