I Electrons in Quantum Field Theory: A Composite Excitation

[Philipsmett]

In qft electron can be considered as composite excitation in several fields?

 

[PeterDonis]

In qft electron can be considered as composite excitation in several fields?

No, it's an excitation of the electron field.

 

[DarMM]

In QED it's an "excitation" of the asymptotic electron fields, which are not the same as the spinor $\psi$ field that appears in the Lagrangian.

However there is much more to it than that, as the details of these asymptotic electron fields are quite complex since they include quantum Coloumb fields (in one formulation) but the full detail would take us into an A-level thread.

 

[king vitamin]

In some sense, I would argue that a physical electron is "composite," in that interactions with the photon field (and really, all other fields in the universe), result in a lone physical electron being an extremely complex composite of the bare fields of your theory. That is, if you wrote down the state of an electron in the Schrödinger representation, defining it as the least massive charge -$e$ eigenstate of the Standard Model Hamiltonian, it would be a nontrivial wave functional of the electron and photon fields (and once again, some small contribution from all other fields).

Things get a little subtle because you often want to define "renormalized" fields, and I believe you can do so such that the physical electron is purely made up by an appropriately defined "renormalized electron field." This is probably what the earlier comment meant, and that's not an incorrect view. We are free to redefine which fields we call "fundamental" however we want.

This all also raises the question about how one wants to define QFT non-perturbatively. I tend to think of physical theories with a UV regulator, and this introduces some ambiguity (due to choice of regulator) in all results, which should drop out of low-energy observables.

 

[PeterDonis]

Things get a little subtle because you often want to define "renormalized" fields, and I believe you can do so such that the physical electron is purely made up by an appropriately defined "renormalized electron field." This is probably what the earlier comment meant

Yes, that's basically what I meant. There are, of course, plenty of complexities lurking underneath, but as @DarMM pointed out, those complexities would probably take us into A-level territory.

 

[DarMM]

That is, if you wrote down the state of an electron in the Schrödinger representation, defining it as the least massive charge -ee eigenstate of the Standard Model Hamiltonian, it would be a nontrivial wave functional of the electron and photon fields (and once again, some small contribution from all other fields).

Things get a little subtle because you often want to define "renormalized" fields, and I believe you can do so such that the physical electron is purely made up by an appropriately defined "renormalized electron field."

Yes basically. Though the field of that electron is an excitement of is a much more complex object than $\psi_R$, the renormalized version of the Lagrangian spinor field. However these fields are very complex mathematically and have electromagnetic properties very different from what classic electrodynamics would suggest.

This is basically because a proper non-perturbative electron in QED is very different from what it appears like in perturbative QED, fortunately the details don't affect perturbative scattering calculations, so aren't relevant to most experiments.

 

[Philipsmett]

Yes basically. Though the field of that electron is an excitement of is a much more complex object than $\psi_R$, the renormalized version of the Lagrangian spinor field. However these fields are very complex mathematically and have electromagnetic properties very different from what classic electrodynamics would suggest.

This is basically because a proper non-perturbative electron in QED is very different from what it appears like in perturbative QED, fortunately the details don't affect perturbative scattering calculations, so aren't relevant to most experiments.

If an electron can be a combination of different fields, can electrons interact not only through an electromagnetic force, but also through a strong or weak force?

 

[DarMM]

Well the electron interacts with the weak force, you'd see this just from the standard model interaction terms even without going into what fields it's an excitement of.

The electron is an excitement of several of the Lagrangian fields, but at the same time is also an excitation of a single electron field that one can define, even though this field doesn't appear in the Lagrangian. So whether it's an excitation of one or several fields depends on what you take as your fundamental fields when writing the theory.

 

[Philipsmett]

Well the electron interacts with the weak force, you'd see this just from the standard model interaction terms even without going into what fields it's an excitement of.

The electron is an excitement of several of the Lagrangian fields, but at the same time is also an excitation of a single electron field that one can define, even though this field doesn't appear in the Lagrangian. So whether it's an excitation of one or several fields depends on what you take as your fundamental fields when writing the theory.

Tell me, for example, if an electron is the excitation of several fields, can it lose its charge?

 

[DarMM]

Tell me, for example, if an electron is the excitation of several fields, can it lose its charge?

No, that's conservation of electric charge.