A gravitationally induced decoherence model for photons in the context of the relational formalism

TL;DR

This work derives a field-theoretic master equation for gravitationally induced decoherence of photons by starting from Maxwell theory coupled to linearised gravity in Ashtekar-Barbero variables and treating gravity as an environment in a post-Minkowskian expansion. Using the relational (clock-based) formalism, the authors construct Dirac observables via a Kuchař decomposition with geometrical clocks and a U(1) Gauß clock, obtaining a physical Hamiltonian that includes true interactions and a gravity-induced self-interaction term. After a Fock quantisation of the reduced system, they derive a time-convolutionless master equation for the photon sector, with environment correlation functions computed from a thermal gravitational background; the resulting equation shares structural features with scalar-field results but with a vector-field-specific operator structure. The approach is gauge-invariant and compatible with future LQG-inspired quantisation, and it provides a concrete framework to study renormalisation and the regime of validity of Markov/Rotating Wave approximations in relativistic open quantum systems, with potential extensions to fermions and phenomenological bounds from experiments.

Abstract

We formulate a model of gravitationally induced decoherence for photons starting from Maxwell theory coupled to linearised gravity, expressed in terms of Ashtekar-Barbero variables and treated as an open quantum field theoretic system. In contrast to quantum mechanical models, the interaction between the system (Maxwell field) and the environment (gravitational field) is not postulated phenomenologically, but is instead dictated by the underlying action in a post-Minkowskian approximation. This framework extends earlier models for a scalar field and enables a more detailed analysis of the role of dynamical reference fields (clocks) within the relational formalism. We show that, for a suitable choice of geometrical clocks together with a U(1)-Gauss clock, and by employing an appropriate combination of the observable map and its dual, the resulting Dirac observables are given directly by the transverse components of the photon field as well as the symmetric-transverse-traceless degrees of freedom of gravitational waves on the linearised phase space of the coupled system. In addition we also compare different choices of Dirac observables and their dynamics. Upon applying a Fock quantisation to the reduced system, we derive the time convolutionless (TCL) master equation, truncated at second order, and analyse its structural properties. These results provide a foundation for further investigations of the decoherence model, including its renormalisation and a detailed study of its one-particle sector, and are found to be structurally consistent with former master equations for photons derived using ADM variables and a specific gauge fixing.