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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Decoherence in quantum electrodynamics and quantum gravity

Claus Kiefer

Published Aug 15, 1992• 116 citations
Publisher

Abstract

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 Schr\"odinger 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.

DOI
10.1103/physrevd.46.1658

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In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement outcomes. It has recently been shown that covariant classical-quantum dynamics can be constructed using path integral methods, with the dynamics encoded in a combined action for the classical and quantum variables. This work introduces a classical-quantum model whereby quantum gravity interacts with a classical scalar field. The scalar field can be viewed as fundamentally classical or effectively classical due to the decoherence of a quantum gravity theory. The dynamics act to collapse quantum spacetimes according to their Ricci scalar, with corresponding diffusion in the scalar field due to the quantum back-reaction. In the classical limit, the diffusion in the scalar field manifests itself via stochastic fluctuations in the Newtonian potential. Because we couple a classical scalar field to perturbative quantum gravity, we find the theory is not renormalizable but is instead to be viewed as an effective field theory. However, it is an effective field theory that does not necessarily require a measurement postulate. More generally, our work shows it is possible to integrate collapse dynamics with high-energy physics and covariance.