How does QED explain the circular magnetic field around a straight conductor?

Since Maxwell's equations are phenomenological, I'm looking for the actual deep reason why the magnetic field is oriented circularly around a straight conductor.

Could anybody knowledgeable on quantum electrodynamics please elaborate on this subject? Is there an explanation, or does QED itself depend on Maxwell's description, without offering some particular underlying mechanism?

(Alternatively, or complementarily, does general relativity offer some explanation for the circular geometry of the magnetic field lines?)

• Does this answer your question? How do you go from quantum electrodynamics to Maxwell's equations? Apr 4, 2022 at 9:19
• QED is a theory to calculate scattering probabilities. It cannot be used to calculate magnetic field lines, or at least not directly. However when we require that QED has a U(1) local gauge symmetry this requires us to introduce a field that turns out to be the electromagnetic four potential used in Maxwell's equations, and this does predict circular magnetic field lines. So reducing QED to classical EM is the answer to your question and the linked question is indeed a duplicate. Apr 4, 2022 at 9:35
• @shredEngineer The only image I could find after a quick search was this one, though it's a bit sparse for my liking. Hopefully you can still see why it is a more "natural" picture than the typical one. But a bivector should be visually intuitive: it is a oriented (i.e. swirling) plane segment, just like a vector is an oriented (i.e. directional) line segment.
– HTNW
Apr 4, 2022 at 11:18
• these may help you with the bi-vector concept: physics.stackexchange.com/questions/160993/… and physics.stackexchange.com/questions/410714/… Apr 4, 2022 at 13:39
• @shredEngineer If you want to learn more about the general subject of bivectors there is a nice YouTube video on geometric algebra here. Apr 4, 2022 at 16:06