I Is the electromagnetic field of an electron in QFT a real physical field?

[Philipsmett]

According to the QFT, each electron creates an electromagnetic field around itself. Is this field real or is it just a virtual mathematical field?

 

[Vanadium 50]

How do you distinguish real fields from mathematical fields?

 

[Philipsmett]

How do you distinguish real fields from mathematical fields?

I'm asking you

 

[PeterDonis]

I'm asking you

If you can't give a way to distinguish "real fields" from "virtual mathematical fields", then your question is meaningless and we can't answer it. You need to explain what you mean by those two terms for us to be able to answer your question.

 

[Philipsmett]

If you can't give a way to distinguish "real fields" from "virtual mathematical fields", then your question is meaningless and we can't answer it. You need to explain what you mean by those two terms for us to be able to answer your question.

I ask whether the electromagnetic field of an electron in QFT is a real physical field, or this is an imaginary field for computation as a virtual photons.

 

[_PJ_]

The electron (as a disturbance i the electron field) interacts with electromagnetic field and therefore there are disturbances in the electromagnetic field (photons) Further, since photons are electromagnetic and electrons are charged, they respond to this and there are further disturbances ad infinitum.

Mathematically, the equations can determine the effect of these disturbances but this requires an infinite amount of possible interactions - however, the "significance" of these interactions' influence becomes lesser and lesser so these interactions can be approximated.

This is typically visualised with Feynman diagrams which show the broader approximation of the aggregate results of these infinite influences whislt also allowing one to (should one wish) add details to represent levels of energy resolution to incorporate more vertices and propagations within the diagram which is pictorally showing complexities in the system pertaining to the distrbutions of energy.

The mathematics bear out to incredibly accurately align with a macroscopic measurement so it is a good model of reality.

However, since the EM disturbances (i.e. photons) that are "generated by" and "interacting with" the electron in a loop of self-interaction can never be observed directly, they are often referred to as "virtual".

This is my understanding at least, I hope that this is correct -apologise for my lack of technical terms or correct vocabulary) and welcome corrections and clarifications.

 

[Vanadium 50]

You're simply repeating your question.

I suspect that the reason you are struggling to explain the difference you are trying to draw is that it is not clear in your own mind.

 

[PeterDonis]

I ask whether the electromagnetic field of an electron in QFT is a real physical field, or this is an imaginary field for computation as a virtual photons.

And, as @Vanadium 50 has pointed out, this just restates your question without explaining what you think the difference is. So your question can't be answered.

Thread closed.

 

[PeterDonis]

Moderator's note: Thread reopened by request.

 

[strangerep]

According to the QFT, each electron creates an electromagnetic field around itself. Is this field real or is it just a virtual mathematical field?

In the usual textbook presentations of QED, one starts with free electron fields and free photon fields. The electron and photon fields commute, which essentially means they're independent of each other. Then one adds an interaction term in the Hamiltonian (essentially a product of the photon field and the electron current field). In standard perturbative scattering theory, you'll see diagrams with "virtual photons", etc, which are just mathematical abstractions denoting terms in a perturbation series.

However, one can alternatively re-define the fields in the full interacting theory such that the original electron field is replaced by a product of that and a coherent state of the photon field. One calls this a "dressed" electron field. It's more physically intuitive since the commutator between the dressed electron and the ordinary photon field yields a result essentially equivalent to the usual Coulomb electric field we normally associated with a point charge.

In other words, in an interacting QFT there is typically some flexibility in how one delineates which basic fields one would like to work with. Different choices have their strengths and weaknesses.

[Btw, this answer might not be directly suitable for an "I" level thread. If so, perhaps you should tell us which QFT textbooks you've been studying.]

HTH.

 

[bhobba]

Its usually thought of as real because of Noether's theorem it carries energy and momentum which, since physicists are simple souls most would consider real. For example mass is thought of as real and since mass is a form of energy its hard not to think of it as real as well. But as has been correctly pointed out - what is real? It's a philosophical question not really important to physics, much more important to philosophy, and we do not discuss philosophy here.

 

[vanhees71]

I ask whether the electromagnetic field of an electron in QFT is a real physical field, or this is an imaginary field for computation as a virtual photons.

As soon as somebody tells you to think about what's real in physical theories, be very careful not to be confused. The notion of "reality" is a philosophical notion and thus doomed to be so unclearly defined that one can say it's not defined at all.

For a physicist something is "real", if it can be unambiguously and objectively measured.

Now the electromagnetic field is first of all a motion within classical physics dealing with macroscopic charges and currents. It's operationally defined in the above sense by the forces acting on test charges. By definition a "test charge" is a charge so small and at far enough distance from the charges and currents that are the sources of the em. field you want to measure that their influence on the sources can be neglected. Then and only then the fields (like the Coulomb field of a source charge sitting somewhere at rest) are well-defined by the force law
$$\vec{F}=q(\vec{E}+\vec{v} \times \vec{B}),$$
where $q$ is the test charge and $(\vec{E},vec{B})$ the electromagnetic field to be defined by this force on the test charge.

Now if you have an electron, it's impossible to define the electromagnetic field caused by it as a source since there's nothing with a charge much smaller than the charge of the electron you can use as a test charge, i.e., there's no way to measure the electromagnetic field of a single electron without disturbing the very electromagnetic field you want to measure, and that's why the electromagnetic field is not so easy to define as a direct observable in Quantum Electrodynamics.

What is well-defined in QED are (a) S-matrix elements describing measurable quantities like cross sections of scattering events like elastic electron-electron scattering or Compton scattering or annihilation of an electron and a positron, the creation of one or more additional photon in scattering of charged particles (bremsstrahlung), etc. etc. or (b) certain correlation functions in the case of relativistic many-body QFT as in quantum optics. When dealing with single photons you can derive the probability with which they are detected running through some optical devices etc. But also there it's hard to conceive how to define the "electromagnetic field" as such. On the other hand, if you use a laser, the emitted light is well described by a classical electromagnetic field. Quantum-field-theoretically it's a socalled "coherent state", which has no well-defined photon number but is a superposition of states of all photon numbers.