Luis Fernando Urrutia

Duality for symmetric second rank tensors. II. The linearized gravitational field

The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples illustrating the general procedure and the physical interpretation of the dual fields. The zero mass case of the massive theory dual to the massive spin-two theory is also examined, but we show that it only contains a spin-zero excitation.

BRST-BFV method for nonstationary systems.

Starting from an associated reparametrization-invariant action, the generalization of the BRST-BFV method for the case of nonstationary systems is constructed. The extension of the Batalin-Tyutin conversional approach is also considered in the nonstationary case. In order to illustrate these ideas, the propagator for the time-dependent two-dimensional rotor is calculated by reformulating the problem as a system with only first class constraints and subsequently using the BRST-BFV prescription previously obtained.

Quantum Gravity Phenomenology

The old order of magnitude argument stating that physics from Planck scale is out of experimental reach has been reconsidered in recent years in the light of current astrophysical and high precision tests indicating possible enhancement of the otherwise tiny quantum gravity effects. Nowadays it seems feasible to probe and discard effects associated with some simplified models and situations describing the space time structure at Planck length by these means. In this work we intend to survey contributions that have been developed by at least one collaborator researcher working in Mexico, but showing them within the whole framework of the field. The corresponding list of works start from Ref.[57] on. As in any paper of this kind an inevitable or even not adverted biased point of view can appear in spite of our efforts to avoid it. Clearly our list of references is incomplete and we apologize in advance for omissions due mainly to lack of space.

Reality conditions as second class constraints

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions.