Instantaneous communication, Aharanov-Bohm and the Coulomb Gauge

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SUMMARY

The discussion centers on the implications of the Coulomb gauge in quantum electrodynamics (QED) and its relationship with the Aharonov-Bohm effect. It asserts that changes to scalar and vector potential fields in the Coulomb gauge propagate instantaneously, raising questions about causality. The conversation highlights that despite this instantaneous propagation, the interference pattern of particles passing around a magnetic field does not reflect immediate changes, thus preserving Poincare covariance in QED. The conclusion is that QED in the Coulomb gauge remains Poincare invariant, even if this invariance is not explicitly evident in the equations.

PREREQUISITES
  • Understanding of quantum electrodynamics (QED)
  • Familiarity with the Aharonov-Bohm effect
  • Knowledge of Poincare invariance and its significance in physics
  • Basic concepts of gauge theories, specifically the Coulomb gauge
NEXT STEPS
  • Explore the mathematical framework of the Aharonov-Bohm effect
  • Study the implications of Poincare covariance in quantum field theories
  • Investigate the role of scalar and vector potentials in gauge theories
  • Examine the operator algebra in quantum electrodynamics for anomaly-free conditions
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and field theory, as well as students and researchers interested in the foundational aspects of gauge theories and their implications for causality and invariance in physics.

maverick_starstrider
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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?
 
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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.
 

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