  We show that the Power-Zienau-Woolley picture of the electrodynamics of
nonrelativistic neutral particles (atoms) can be derived from a gauge-invariant
Lagrangian without making reference to any gauge whatsoever in the process.
This equivalence is independent of choices of canonical field momentum or
quantization strategies. In the process, we emphasize that in nonrelativistic
(quantum) electrodynamics, the all-time appropriate generalized coordinate for
the field is the transverse part of the vector potential, which is itself gauge
invariant, and the use of which we recommend regardless of the choice of gauge,
since in this way it is possible to sidestep most issues of constraints.
Furthermore, we point out a freedom of choice for the conjugate momenta in the
respective pictures, the conventional choices being good ones in the sense that
they drastically reduce the set of system constraints.
