Instantaneous communication, Aharanov-Bohm and the Coulomb Gauge

[maverick_starstrider]

I'm just curious, in the Coulomb gauge changes made locally to the scalar and vector potential fields are propagated instantaneously, classically we wave off this problem since the potentials aren't directly observable... except they are in Aharanov-Bohm. Presumably there's something that saves causality but what is it? If I pass two particles either way around an enclosed magnetic field, why can't changes in this magnetic field be instantaneously recognized in the interference pattern when the two particles are recombined?

 

[tom.stoer]

In order to check for Poincare covariance in QED you have to calculate all Poincare generators and check their algebra. It's a messy calculation but you will find that the Poincare algebra is satisfied, therefore
a) the operator algebra is anomaly-free and
b) the Hilbert space carries representations of the Poincare algebra.

Therefore QED in Coulomb gauge is Poincare invariant even if this is not directly visible in the formulas.