Reparametrization Invariance and the Schr\"odinger Equation

In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schr\"odinger equation. The procedure is applicable in the supersymmetric theories as well. The $n=2$ supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schr\"odinger equation.Comment: RevTeX,25 page

Affine semigroups having a unique Betti element

We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its Application

The oxygen abundance in the IFU era

Spatially-resolved information of gas-phase emission provided by integral field units (IFUs) are allowing us to perform a new generation of emission-line surveys, based on large samples of HII regions and full two-dimensional coverage. Here we present two highlights of our current studies employing this technique: 1) A statistical approach to the abundance gradients of spiral galaxies, which indicates an -universal- radial gradient for oxygen abundance; and 2) The discovery of a new scaling relation of HII regions in spiral galaxies, the "local" mass-metallicity relation of star-forming galaxies.Comment: 6 pages, to appear in Highlights of Spanish Astrophysics VII, Proceedings of the X Scientific Meeting of the Spanish Astronomical Society held on July 9-13, 2012, in Valencia, Spai

Metafísica del cuerpo y de la historia: Charles Péguy

Desde Aristóteles, y quizá desde Platón, la metafísica ha sido entendida como el estudio del ente inmóvil. El ser metafísico es considerado por esa tradición como aquel que está fuera de la naturaleza del movimiento y que, por lo tanto, no goza de una historicidad, dejando así fuera de consideración la situación encarnada del hombre. Intento explicar en este artículo cómo Charles Péguy rompe con la metafísica de la inmovilidad y permite establecer una metafísica encarnada, del cuerpo y de la historia, una metafísica que hace mayor justicia al problema del hombre. Since Plato and Aristotle, tradition has considered Metaphysics as the science of the immobile being. The being of Metaphysics is, in this tradition, the one that is out the nature of movement and, thus, has no historicity, leaving without consideration the incarnated situation of man. I try to explain in this article the way in which Charles Péguy breaks this Metaphysics of immobility and allows to establish the Metaphysics of incarnation or embodiment, of body and history, an adequate Metaphysics to the problem of man