The logical consistency of a description of quantum theory in the context of general relativity, which includes minimal coupling principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will argue from this standpoint and use an argument that claims the incompleteness of the general relativistic description of gravitation, which emerges as a consequence of the gravitationally induced phases of the so-called flavor-oscillation clocks, that the postulates of quantum theory are logically incompatible with the usual minimal coupling principle. It will be shown that this inconsistency could emerge from the fact that the required geometrical information to calculate the probability of finding a particle at any point of the respective manifold does not lie in a region with finite volume. Then we put forth a new quantum minimal coupling principle in terms of a restricted path integral, and along the ideas of this model not only the propagator of a free particle is calculated but also the conditions under which we recover Feynman's case for a free particle are deduced. The effect on diatomic interstellar molecules is also calculated. The already existing relation between restricted path integral formalism and decoherence model will enable us to connect the issue of a quantum minimal coupling principle with the collapse of the wave function. From this last remark we will claim that the geometrical structure of the involved manifold acts as, always present, a measuring device on a quantum particle. In other words, in this proposal we connect the issue of a quantum minimal coupling principle with a claim which states that gravity could be one of the physical entities which results in the collapse of the wave function. * E-mail: acamacho@aip.de 275 Mod. Phys. Lett. A 1999.14:275-288. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only.

The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an example, the case of a particle whose coordinates are being monitored. Employing the so-called restricted path integral formalism, it will be shown that the measuring process could always contain information concerning the gravitational field. In other words, it seems that with the presence of a measuring process the equivalence principle may, in some cases, break down. The relation between the breakdown of the equivalence principle, at quantum level, and the fact that the gravitational field could act always as a decoherence environment, is also analyzed. The phenomena of quantum beats of quantum optics will allow us to consider the possibility that the experimental corroboration of the equivalence principle at quantum level could be taken as an indirect evidence in favor of the quantization of the gravitational field, i.e., the quantum properties of this field avoid the violation of the equivalence principle.

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11 2 Teorías multidimensionales y rompimiento espontáneo de la simetría . 31