Are there asymptotic QTF/QED states in a constant magnetic field?

[gentzen]

It is "easy" to produce experimental setups that could and should for all practical purposes be described as having a constant background magnetic field everywhere, especially in the "asymptotic region" where the detectors are located.

You can do this both in vacuum, and inside a solid sample. In a solid sample, the effect of the constant magnetic field is "basically clear" and "well studied", i.e. you get a circular motion, and if the radii of that motion are bigger that the sample, then you get "scattering effects" at the boundary of the sample. In vacuum, the meaning of such asymptotic states seems less clear to me than in a solid sample, because there are is no sample size and no boundaries, for "comparison".

On the ofther hand, I guess that QFT/QED has no problems in principle to describe such "easy to produce" experimental situations. But how is this actually done?

 

[vanhees71]

You just have a "semiclassical model", i.e., you introduce the classical em. field as an classical "c-number background field". Then you can do perturbation theory for particles (in QED usually electrons and positrons) and the em. field (photons) as usual. You only have to solve for the modes (energy-eigenmodes) including the classical background field.

 

[gentzen]

You just have a "semiclassical model", i.e., you introduce the classical em. field as an classical "c-number background field". Then you can do perturbation theory for particles (in QED usually electrons and positrons) and the em. field (photons) as usual. You only have to solve for the modes (energy-eigenmodes) including the classical background field.

Good to hear that this "can be done in principle", like I guessed.

But how do you deal with the circular (or spiral) motion of the asymptotic states caused by the magnetic field? Do you just take the resulting quantization into account, like for the quantum Hall effect in a "sufficiently big" solid sample? Or do you "cut open" the circles at the half-space defined by the (flat) detector surface? (Or is it enough to just focus on spiral motion sufficiently different from circular motion to not cause relevant quantizations? That would somehow feel "wrong" to me.) Or ... ?

 

[vanhees71]

In a magnetic field the energy eigenmodes represent particles that in the classical analogue move on spirals. Asymptotic free states represent particles interacting only with the classical background-magnetic field but are not subject to collisions.

 

[gentzen]

In a magnetic field the energy eigenmodes represent particles that in the classical analogue move on spirals. Asymptotic free states represent particles interacting only with the classical background-magnetic field but are not subject to collisions.

Ok, so "you just take the resulting quantization into account". I guess it makes sense, because the typical "experimental scattering in vacuum setup" will probably not depend on the boundaries in a systematical way. And the "spurious" quantization(s) will have nearly no impact in the results, because they are more a property of some simple canonical basis, and less relevant for the actual physical situation. (I remember "related" discussions about fast electrons in solids, and why one doesn't need to worry the ambiguity of the wavevector for Bloch waves, because it doesn't make a difference for the actual physical situation, which is represented by appropriate superpositions, instead of the basis functions themselves.)

One reason why I "guessed" that one would prefer states that don't need to satisfy global constraints was that the typical situation for a classical background is gravity, and there the background is typically defined only locally, at least the relevant background. And the situation with the constant magnetic field is somewhat similar, because again only the locally constant magnetic field is relevant. But since it is easy to continue it globally, and it probably preserves more symmetries, it will probably make the math a bit simpler to work with global states.