On the Hamiltonian formulation of Yang--Mills gauge theories

The Hamiltonian formulation of the theory of J-bundles is given both in the Hamilton--De Donder and in the Multimomentum Hamiltonian geometrical approaches. (3+3) Yang-Mills gauge theories are dealt with explicitly in order to restate them in terms of Einstein-Cartan like field theories.Comment: 18 Pages, Submitted to International Journal of Geometric Methods in Modern Physic

General Relativity as a constrained Gauge Theory

The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory.Comment: 8 Pages, Submitted to International Journal of Geometric Methods in Modern Physic

f(R) cosmology with torsion

f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard General Relativity. Only for f(R)=R^{2}, torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f'(R), which can be expressed also as a nonlinear function of the trace of the matter energy-momentum tensor. We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f(R) gravity, torsion can be a geometric source for acceleration.Comment: 13 page

A first-order purely frame-formulation of General Relativity

In the gauge natural bundle framework a new space is introduced and a first-order purely frame-formulation of General Relativity is obtained.Comment: 9 Pages, Submitted to Classical and Quantum Gravit

Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions

We present a Green's function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in a mesoscopic system of N Fermi particles moving independently in a linear potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux and kinetic energy densities as well as their quantal mean-square fluctuations. We also study some properties of the kinetic energy functional E_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic energy density yields a multi-valued function, an exact single-valued relationship between the density derivative of E_{kin}[n(x)] and the particle density n(x) is demonstrated and evaluated for various values of the number of particles in the system.Comment: 10 pages, 5 figure

Ensayo de vida de lámparas halógenas de bajo voltaje con reflector dicroico

El uso masivo que se ha producido en el Uruguay de la lámpara halógena de bajo voltaje con reflector dicroico (generalmente llamada lámpara dicroica) ha despertado el especial interés de proyectistas y técnicos en iluminación respecto a las características particulares de estas lámparas, en especial, en lo que se refiere a su vida media. Se ha observado que en muchas instalaciones donde se han utilizado estas lámparas la frecuencia de falla ha sido muy superior a la esperada. Por otra parte, se ha observado una gran dispersión de estos valores dependiendo del fabricante, aún en los casos en que la vida media nominal especificada por todos ellos era la misma. El Grupo LUXROU, integrado por profesionales que trabajan en iluminación y por docentes del Grupo de Fotometría e Iluminación de la Facultad de Ingeniería, se propuso realizar un ensayo de vida a tensión nominal controlada, tomando una muestra de lámparas de todos los fabricantes disponibles en el Uruguay, resultando en un total de 60 lámparas ensayadas. Luego de aproximadamente dos años de ensayos se presentan en este trabajo los resultados del mismo. Se realiza un especial análisis de la evolución del flujo de las lámparas, realizando una comparación con la evolución esperada, utilizando los datos disponibles del fabricante. Asimismo se muestran los momentos de muerte de las lámparas y la evolución de las características del reflector dicroico. Por otra parte, y como consecuencia de la experiencia obtenida, se analizan cuáles deben ser las mejores condiciones de instalación para estas lámparas de forma de asegurar un desempeño adecuado de las mismas

Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap

We derive simple analytical expressions for the particle density $\rho(r)$ and the kinetic energy density $\tau(r)$ for a system of noninteracting fermions in a $d-$dimensional isotropic harmonic oscillator potential. We test the Thomas-Fermi (TF, or local-density) approximation for the functional relation $\tau[\rho]$ using the exact $\rho(r)$ and show that it locally reproduces the exact kinetic energy density $\tau(r)$, {\it including the shell oscillations,} surprisingly well everywhere except near the classical turning point. For the special case of two dimensions (2D), we obtain the unexpected analytical result that the integral of $\tau_{TF}[\rho(r)]$ yields the {\it exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio