The possible description of the vacuum of quantum gravity through the so called κ-Poincaré group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the κ-Poincaré group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the κ-Poincaré group contains some of the physical information of the quantum gravity vacuum, then this vacuum could entail decoherence. This last result will also allow us to consider the possibility of analyzing the continuous measurement problem of quantum theory from a group-theoretical point of view, but now taking into account the κ-Poincaré symmetries.

We calculate the propagator of a particle caught in a Paul trap and subject to the continuous quantum measurement of its position. The probabilities of the measurement outputs, the possible trajectories of the particle, are also found. This enables us to propose a series of experiments that would allow to confront the predictions of one of the models that describe the interaction between a measured quantum system and measuring device, namely the so called Restricted Path-Integral Formalism, with the experiment.

The limitations and possibilities that the concept of quantum interference offers as a tool for testing fundamental physics are explored here. The use of neutron interference as an instrument to confront against measurement readouts some of the principles behind metric theories of gravity will be analyzed, as well as some discrepancies between theory and experiment. The main restrictions that this model embodies for the study of some of the features of the structure of space-time will be explicitly pointed out. For instance, the conditions imposed by the necessary use of the semiclassical approximation. Additionally, the role that photon interference could play as an element in this context is also considered. In this realm we explore the differences between first-order and secondorder coherence experiments, and underline the fact that the Hanbury-Brown-Twiss effect could open up some interesting experimental possibilities in the analysis of the structure of space-time.The void, in connection with the description of wave phenomena, implicit in the principles of metric theories is analyzed. The conceptual difficulties, that this void entails, are commented.

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied. *

Sagnac interferometry has been employed in the context of gravity as a proposal for the detection of the so called gravitomagnetic effect. In the present work we explore the possibilities that this experimental device could open up in the realm of non-Newtonian gravity. It will be shown that this experimental approach allows us to explore an interval of values of the range of the new force that up to now remains unexplored, namely, λ ≥ 10 14 m.

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Transient hydraulics always characterizes the circulating flow during managed pressure drilling. Therefore, the application of the Godunov scheme to oil-well drilling hydraulics is presented. The numerical model developed describes the treatment process of the initial and boundary conditions from the well geometry and true operational conditions. The well-known finite-volume method and Riemann problem are utilized for building the set of discrete equations. The account of Godunov's simulation describes the profiles of transient pressure and transient flow rate along the well. For attending the oil-field engineering concerns, the drilling parameters discussed are as follows: choke pressure, pumping pressure, bottom-hole pressure, and circulating flow rate. After the comparison between computed and well data, the results show a small difference of less than 7 and 1 % for pumping and bottomhole pressures, respectively. The main engineering contribution of this work is the solution and application of the first-order Godunov scheme to analyze the transient hydraulics during actual oil-well drilling and also the analysis and interpretation of the pressure wave behavior traveling along the well. The Godunov scheme has high-potential engineering applications for modeling the transient drilling hydraulics, i.e., controlled flow, underbalanced drilling, and foam cementing, as well.