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.
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