Statistical approach for quantum gravity fluctuations in QFT

The consequences of gravitational zero point quantum fluctuations at Planck scale are considered in the QFTs by adopting an effective stochastic model for space-time. A kinematical approach is used instead of the usual dynamical attempts. The physical quantities are associated to an average over such fluctuations. In particular, the fields have their spectral representation modified. The class of representative field is changed for the description of a field theory and the all order correlation functions, including the two-point functions, are cosequently changed. The investigation of the effect upon QFT succeeded in generating a consistent and more regular theory. In such a scheme the ultraviolet divergences are controlled. Although general, the derivation is performed for scalar Fields. The model is shown to be independent of the specific form of a quantum gravitation theory.