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Implications of gauge freedom for nonrelativistic quantum electrodynamics

Adam Stokes* and Ahsan Nazir†

Adam Stokes*

  • Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom and School of Mathematics, Statistics, and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom

Ahsan Nazir†

  • Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

  • *adamstokes8@gmail.com
  • †ahsan.nazir@manchester.ac.uk
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Rev. Mod. Phys. 94, 045003 – Published 3 November, 2022

DOI: https://doi.org/10.1103/RevModPhys.94.045003

Abstract

Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This relativity is eliminated only 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. It is shown 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 localization and its electromagnetic dressing. 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 are reviewed.

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Rev. Mod. Phys. 94, 045003– Published 3 November, 2022
  • Received 10 February 2021
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