Group-theoretical structure of quantum measurements and equivalence principle

The transverse group associated to some continuous quantum measuring proces ses is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an example, the case of a particle whose coordinate s are being monitored. Employing the so-called restricted path integral for malism, it will be shown that the measuring process could always contain in formation 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 equivale nce principle, at quantum level, and the fact that the gravitational field could always act as a decoherence environment, is also analyzed. The phenom ena of quantum beats of quantum optics will allow us to consider the possib ility that the experimental corroboration of the equivalence principle at q uantum level could be taken as an indirect evidence in favor of the quantiz ation of the gravitational field, i.e. the quantum properties of this field avoid the violation of the equivalence principle.