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In QED, the source of the gauge field (is the gauge field different from the vector potential?) is the current and charge density j, ρ. When a particle (electron) couples to the gauge field (photons), a gauge transformation occurs. A gauge transformation in QM involves both the vector potential and the charged particle. It consists of the joint operation A -> A+ ∂χ (where A is the vector potential) and ψ -> Uψ where U is the phase factor = e(iq/hcχ) for the charged particle. The quantum phase factor is e(-iq/hc) which is a compact representation of the group U1, all rotations about a fixed axis.

1) Does gauge symmetry refer to the term χ acting both on the vector potential and the phase of the charged particle?

When the vector potential climbs or falls a gauge fiber, the phase makes corresponding changes around the ring.

2) Is this is what Feynman does with his clocks…changing the vector potential changes the phase, causing the clock to spin..although Feynman’s clocks seemed associated with photons, not particle phases…).

3) The vector potential seems to only affect the phase of the particle, which doesn’t affect its energy. How is the energy of the particle, (for example when an electron accepts a photon it can jump to a higher orbital/energy level), modeled through interactions with the gauge field?

I'm a biologist trying to get a handle on qft for a project I'm doing.

Thanks very much, I've enjoyed this forum.