Decoherence in quantum electrodynamics and quantum gravity

We treat the interaction of a semiclassical electromagnetic field with a complex scalar field as a continuous measurement process through which certain interference terms between electromagnetic field states may become suppressed—they "decohere." The formal framework is the functional Schrödinger picture for scalar QED. The reduced density matrix for the electromagnetic field is discussed in detail. We calculate the remaining coherence width for realistic laboratory field strengths. The back reaction of the scalar field on the electromagnetic state is discussed with the help of the Wigner function and is explicitly calculated. We compare our results with the corresponding case in quantum gravity where the radius of the Universe is "measured" by inhomogeneous scalar field modes. We propose to render the decoherence factor finite by summing over a set of rescaled field modes.