Quantum measurements and the κ-Poincaré group

Abstract

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.

Theory of radiation and absorption of deformed field quanta

“…The equation of motion of such a field has been studied in [5,6], where the Hamiltonian was presented as an expansion in ordinary annihilation and creation operators. The field equations are non-linear but can be treated perturbatively.…”

“…Obviously, in this case we have the deformation of the field itself rather than the deformation of the real space. This model of electromagnetic field has been considered in [5,6]. The Casimir effect in such a deformed field has been studied in [7], where the Casimir energy was calculated for the one-, two, and three-dimensional cases.…”

Yukawa-type potential effects in the anomalistic period of celestial bodies

“…These forces are expected to be significant for pairs of celestial bodies that lie in a mutual distance greater than 10 10 m, or for elementary massive particles separated by distances in a submillimeter range. While some experimental work has already been developed for the second case (see, e.g., Chiaverini et al 2003;Hoyle et al 2004;Smullin et al 2005), the first domain remains almost unexplored (Camacho 2004). Experimental techniques, such as the Sagnac interferometry and future space missions, may be of much help in exploring this range.…”

Yukawa-type effects in satellite dynamics

“…This is known as the geophysical window. The domain λ ≥ 10 14 m remains unexplored (Camacho 2004). Experimental techniques, such as space interferometers, might be a new method for exploring this domain of orbital range.…”