A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = ∂F + f AF arises besides the one of the first order treatment, F = ∂A − ∂A + f AA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is LP ∝ G 2 . In this application the photon mass is estimated. The SU (N ) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.
We investigate the possibility of detecting the Podolsky generalized electrodynamics constant a. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of a. In order to set up bounds for a we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.
This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature.We analyze the form of the second field strenght, G = ∂F + f AF , in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his Generalized Electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behaviour at short distances as well as a meso-large distance modification.
We analyse systems described by first-order actions using the Hamilton–Jacobi (HJ) formalism for singular systems. In this study we verify that generalized brackets appear in a natural way in HJ approach, showing us the existence of a symplectic structure in the phase space of this formalism.
We analyse the Klein–Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.
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