12,062 research outputs found

    Dirac Matrices for Chern-Simons Gravity

    Full text link
    A genuine gauge theory for the Poincar\'e, de Sitter or anti-de Sitter algebras can be constructed in (2n-1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices \Gamma_{ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices \Gamma_{ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical coefficient \alpha_{s}. We then give a general algorithm that computes the \alpha-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B^{ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, "minimal" algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n=25, which easily covers all foreseeable applications of the trace formula.Comment: v2: 6 pages, no figures. Based on talk presented at I Cosmosul, Rio de Janeiro, Brazil, August 2011. v3: references adde

    Economía, política y estado de derecho

    Get PDF
    En este trabajo se sostendrá que podemos hablar de un “Estado de derecho económico” integrado, por una parte, por algunas leyes económicas básicas inmutables y, por otra, por leyes más contingentes y cambiantes que deberían ser definidas gracias a un trabajo adecuado de la razón práctica. En una segunda sección del trabajo se analizará un caso de falta de respeto a ese Estado de derecho económico, especialmente dañino para la cohesión social: la manipulación política de las estadísticas.In dieser Arbeit wird die Auffassung vertreten, dass von einem „wirtschaftlichen Rechtsstaat“ gesprochen werden kann, der sich einerseits auf einige grundlegende und unveränderliche wirtschaftliche Gesetze, und andererseits auf eher konjunkturabhängige und veränderliche Gesetze stützt, die im Rahmen einer angemessenen, von der praktischen Vernunft geleiteten Weise zu definieren sind. Der zweite Teil der Arbeit analysiert einen Fall von Nichteinhaltung dieses wirtschaftlichen Rechtsstaats, der für den sozialen Zusammenhalt besonders schädlich ist: die politische Manipulation von Statistiken.Fil: Crespo, Ricardo Fernando. Universidad Nacional de Cuyo. Facultad de Filosofía y Letras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
    corecore