Decoherence in the Vacuum Polarization of the Photon Field by the Graviton Field Environment

Abstract

The recently developed correlator approach to decoherence enables one to investigate the decoherence of quantum systems in a field theoretic setting. In quantum field theory, all properties of a system are encoded in the infinite hierarchy of the n-point correlation functions (correlators). However, in a realistic experimental setting one can only probe a finite subset of these correlators. This inability in accessing all the information of the system constitutes the heart of the decoherence program. Neglecting observationally inaccessible correlators corresponds to an increase in the entropy of the system as perceived by the observer and hence to decoherence and classicalization.

An interesting investigation given such a framework would be the decoherence of the photon field by the graviton field environment. Since quantum fields by definition reside on space-time, they can’t be isolated from the effects of the graviton field in any experimental setting however carefully they are designed. Therefore the decoherence of the photon field due to its interaction with the graviton field is an intrinsic quantum correction one must take into account in any experimental setup.

This analysis requires the application of field theory in an out-of-equilibrium setting. The Schwinger-Keldysh formalism provides the suitable framework for our purposes. We consider the 2-Particle Irreducible (2-PI) effective action to correctly take into account the perturbative loop corrections to the 2-point correlation function (the photon propagator) induced by the interaction between the photon and the graviton fields.

We include the 1-loop graviton corrections to photon propagator and assume the case when higher order correlations are inaccessible. We work in general covariant gauge and expect the gauge dependency to drop off once the vacuum polarization is calculated. However, the dressed photon propagator turns out to be graviton gauge dependent and this forbids us from making any useful calculations of entropy. A follow-up of this project will be performing these calculations using Dirac quantization or a fully gauge invariant formalism to remove gauge dependency.