  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.
