What types of forces are described in the standard minimal QED Lagrangian?

[LarryS]

TL;DR

How is the magnetic part of the Lorentz Force realized in Q.E.D. via photon exchange, etc.?

In Q.E.D., the electrical part of the Lorentz Force between unlike and like charged particles is realized through the absorption and emission of photons.

How is the magnetic part of the Lorentz Force realized in Q.E.D. via photon activity?

As always, thanks in advance.

 

[PeterDonis]

In Q.E.D., the electrical part of the Lorentz Force between unlike and like charged particles is realized through the absorption and emission of photons.

How is the magnetic part of the Lorentz Force realized in Q.E.D. via photon activity?

Um, by absorption and emission of (virtual) photons?

Why do you think that is not a sufficient explanation for the magnetic part but it is for the electric part? What's the difference?

 

[LarryS]

The Lorentz Force is basically Classical EM, right? In that world, the magnetic force has a velocity dependence. Is that velocity dependence in the Q.E.D. world still represented somehow, or is Q.E.D. only concerned with the net force on the particle?

 

[Vanadium 50]

Is that velocity dependence in the Q.E.D. world still represented somehow, or is Q.E.D. only concerned with the net force on the particle?

"Force" isn't really a thing in QM. And this sentance seems to assume some dichotomy that isn't really there.

 

[LarryS]

Not sure which dichotomy you're referring to. Electrical vs Magnetic?

 

[Vanadium 50]

Not sure which dichotomy you're referring to.

The one you posted and I quoted.

 

[vanhees71]

The elegance of the relativistic description of electrodynamics (no matter whether classical or quantum) is that you don't need the artificial split of the electromagnetic field in electric and magnetic components anymore although this is of course important to understand the phenomenology, but the split indeed is frame dependent.

Writing down the standard minimal QED Lagrangian, i.e., a Dirac field minimally coupled to the em. field, contains all kinds of "forces", i.e., the standard Lorentz force $q \vec{E}+q \vec{v} \times \vec{B}/c$ as well as the "forces" due to the magnetic moment of the electron.

By chance we have a more formal answer in another recent thread:

https://www.physicsforums.com/threads/samalkhaiats-challenge-002.1006325/