Abstract
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.
Highlights
We have shown that the Power–Zienau–Woolley picture can be derived from a gauge-invariant Lagrangian, in a way which does not make reference to any gauge or choice of canonical momentum
For a treatment emphasizing the unitary equivalence between the minimal-coupling and the PZW picture, cf
We briefly react to some central claims of theirs which appear erroneous in the light of our treatment
Summary
It is possible to use a gauge-invariant form of the Lagrangian of the minimal-coupling picture as the starting point of such a derivation. When considering the Lagrangian (13) as the starting point of non-relativistic (or, molecular) quantum electrodynamics in the following, the choice of A⊥ as the field generalized coordinate has nothing to do with gauge fixing, because we do not say that A is zero.
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