Metrical fluctuations and inertial properties of particles

In our approach spacetime fluctuations are described by means of fluctuations of the metric which is given by a weak-field approximation up to second order. On a curved background these terms are regarded as fluctuations of spacetime which are characterized by a Langevin equation leading to a stochastic behaviour which can be modified in order to describe different types of fluctuation scenarios. In this context we calculate a modified Klein-Gordon equation and a modified Schroedinger equation and perform an average over the fluctuations. Alternatively, treating spacetime fluctuations as a heath bath which couples to a quantum system is described in terms of a modified Lagrangian. Effectively, this is a open quantum system leading to a modified quantum master equation. Results are a modified inertial and gravitational mass leading to a violation of the weak equivalence principle and a violation of Lorentz invariance. These modifications are dependent of the fluctuation scenario. (orig.)