Implications of gauge-freedom for non-relativistic quantum electrodynamics

Adam Stokes, Ahsan Nazir

Published 2020-09-22Version 1

We review gauge-freedom in quantum electrodynamics (QED) outside of textbook regimes. We emphasise that QED subsystems are defined {\em relative} to a choice of gauge. Each definition uses different gauge-invariant observables. We show that this relativity is only eliminated if a sufficient number of Markovian and weak-coupling approximations are employed. All physical predictions are gauge-invariant, including subsystem properties such as photon number and entanglement. However, subsystem properties naturally differ for different physical subsystems. Gauge-ambiguities arise not because it is unclear how to obtain gauge-invariant predictions, but because it is not always clear which physical observables are the most operationally relevant. The gauge-invariance of a prediction is necessary but not sufficient to ensure its operational relevance. We show that in controlling which gauge-invariant observables are used to define a material system, the choice of gauge affects the balance between the material system's localisation and its electromagnetic dressing. We review various implications of subsystem gauge-relativity for deriving effective models, for describing time-dependent interactions, for photodetection theory, and for describing matter within a cavity.