Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Instantaneous communication, Aharanov-Bohm and the Coulomb Gauge

  1. Jan 20, 2012 #1
    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?
  2. jcsd
  3. Jan 21, 2012 #2


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook