How does a magnetic feild work?

How does a magnetic field physically attract another magnetic field? I mean does Quantum Electrodynamics explain magnetic fields as well as the EM force? Or is it some kind of different quantum field theory?

How does a magnetic field physically attract another magnetic field? I mean does Quantum Electrodynamics explain magnetic fields as well as the EM force? Or is it some kind of different quantum field theory?

If you expect you will know the "physical" meaning of the magnetic field better using the Quantum Electrodynamics (QED), it will be difficult, I think.
Because the magnetic field of QED also satisfies the Maxwell's equation which is the same as the classical electrodynamics.

For example, the difference between QED and the classical electrodynamics is the existence of the virtual photon and particles.

But we must use the unimaginable idea of the infinite bare charge and mass of the renormalization theory.

The "mathematical" property becomes much stronger in QED.
I think we seem to go away from the actual "physical" imaging of the magnetic field in QED.
Actually, when you open the textbook of QED, there are many "mathematical" wavefunctions in them.