Descripción: We briefly review f(R) theories, both in the metric and Palatini formulations, their scalar-tensor representations and the chameleon mechanism that could explain the absence of perceptible consequences in the Solar System. We also review f(T) theories, a different approach to modified gravity consisting in a deformation of the teleparallel equivalent of General Relativity. We show some applications to cosmology and cosmic strings. As f(R)'s, f(T) theories are not exempted from additional degrees of freedom; we also discuss this still open issue. © 2012 American Institute of Physics.

Descripción: It is well known that - differing from ordinary gauge systems - canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation of the new coordinates is equivalent to the fixation of the original ones; this aim can be achieved only if the Hamiltonian constraint allows for an intrinsic global time. Thus the resulting action, describing an ordinary gauge system and allowing for canonical gauges, can be used in the path integral for the quantum propagator associated with the original variables. © 1997 American Institute of Physics.

Descripción: It is shown that Born-Infeld gravity -a high energy deformation of Einstein gravity-removes the singularities of a cosmic string. The respective vacuum solution results to be free of conical singularity and closed timelike curves. The space ends at a minimal circle where the curvature invariants vanish; but this circle cannot be reached in a finite proper time. © Published under licence by IOP Publishing Ltd.

Descripción: In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime. © 2010 Elsevier B.V.

Descripción: Some conceptual issues concerning f(T) theories - a family of modified gravity theories based on absolute parallelism - are analyzed. Due to the lack of local Lorentz invariance, the autoparallel frames satisfying the field equations are evasive to an a priori physical understanding. We exemplify this point by working out the vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies. © 2011 Elsevier B.V.

Descripción: Reducible gauge theories with constraints linear in the momenta are quantized. The equivalence of the reduced phase space quantization, Dirac quantization, and BRST quantization is established, provided one transforms appropriately the Dirac wave functions under changes of representation of the constraint surface and of the reducibility functions. The ghosts of ghosts are found to play a crucial role in the equivalence proof. © 1993 American Institute of Physics.

Descripción: General constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random-phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions. © 1995 American Institute of Physics.