Identification of Poincare-gauge and multipolar nonrelativistic theories of QED

Abstract

For over six decades, quantum electrodynamics (QED) in multipolar form has been an invaluable tool for understanding quantum-scale atomic and molecular interactions. However, its relation to the Poincare-gauge has been a recent topic of controversy and debate. It was claimed by Rousseau and Felbacq in the article Scientific Reports 7, 11115 (2017) that Hamiltonian multipolar QED is not the same as Poincare-gauge QED and that it is not generally equivalent to Coulomb-gauge QED. This claim has subsequently been refuted, but since both sides of the debate appear technically sound, a clear reconciliation remains to be given. This task is of paramount importance due to the widespread use of multipolar QED in quantum optics and atomic physics. Here, unlike in other responses, we adopt the same method as Rousseau and Felbacq of using Dirac's constrained quantisation procedure. However, our treatment shows that Poincare-gauge and multipolar QED are identical. We identify the precise source of the apparent incompatibility of previous results as nothing more than a semantic mismatch. In fact there are no inconsistencies. Our results firmly and rigorously solidify the multipolar theory.

arXiv comment8 pages

References in corpus (15)

• Breakdown of gauge invariance in ultrastrong-coupling cavity QED
• Perspective: Quantum Hamiltonians for Optical Interactions
• Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED
• Van-der-Waals potentials of paramagnetic atoms
• Exact electrodynamics versus standard optics for a slab of cold dense gas
• Extending the validity range of quantum optical master equations
• Why you should not use the electric field to quantize in nonlinear optics
• Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall
• Super- and subradiant emission of two-level systems in the near-Dicke limit
• Non-linear non-local molecular electrodynamics with nano-optical fields
• A dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media
• Ultrastrong time-dependent light-matter interactions are gauge-relative
• On the gauge of the natural lineshape
• Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules
• Theory and computation of electromagnetic transition matrix elements in the continuous spectrum of atoms

Cited by in corpus (4)

• Implications of gauge freedom for nonrelativistic quantum electrodynamics
• Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media
• Resonant tunneling diodes in semiconductor microcavities: modeling polaritonic features in the THz displacement current
• A Green-function unification of weak interactions with environmental dressing