# A master equation for gravitationally induced decoherence of a scalar field using Ashtekar variables (Max Fahn, FAU) FAU^2 Talk

In the talk, we present the derivation of a decoherence model containing a scalar field coupled to a gravitational environment. With such models the influence of the quantum gravitational environment on the scalar field’s dynamics can be analysed. Starting with full general relativity in Ashtekar’s connection formulation, we focus on weak gravitational interactions in an asymptotically flat universe and the scalar field as matter component. We apply a reduced phase space quantisation of the model by means of choosing suitable Dirac observables and apply a Fock quantisation to the reduced phase space. The quantised system is then treated as an open quantum system with gravity as the environment. With the help of the projection operator technique, we derive a second order time-convolutionless master equation. This equation is an effective evolution equation which encodes the temporal evolution of the scalar field in terms of certain operators, whose form is a result of the model under consideration and several physical assumptions. These operators arise when taking the trace over the gravitational environment and lead to physical effects like dissipation or 16:45decoherence of the matter field induced by gravity. Finally, we briefly discuss possible applications of the model’s master equation