Thinking about the static electric field in terms of QFT

[FallenApple]

So according to classical electrodynamics, an electron would produce an electric field that is a physical entity in and of itself. This field has momentum so when a test charge is placed within this vicinity, it would be affected by the field itself, not the electron.

But what about the QFT way of looking at it? I've heard that charge is created when the electron field and the electro magnetic field oscillate due to inputing energy. And that this charge happens at a contour of the energy function where the strength of the em field and the electron field are the inputs of the energy function.

So the electron particle is an excitation of the electron field, but what about the excitation of the electromagnetic field? Where does that manifest itself? Is it the static electric field that we always see? But then wouldn't that static "field" then be made of particles since it too is an excitation?

So would the static electric "field" of the electron not be the lowest state of fundamental field itself but an excitation of it? So then it isn't a continuous field per se like the classical image of it.

 

[bahamagreen]

I've wondered a similar thing...
It seems as if the constancy of c was originally attributed to a absolute universal undetectable "static field", then updated by the allocation of individual undetectable "static fields" to frames of reference with constancy of c.

It also seems that originally electrons were allocated individual fields, then updated to a universal electron field within which local excitation represents electrons.

Looks like relativity went one way denying any absolute universal "static fields"... not sure if QFT consider themselves going the other way...?

 

[PeterDonis]

I've heard that charge is created when the electron field and the electro magnetic field oscillate due to inputing energy.

Please give a specific reference. This doesn't look right.

the electron particle is an excitation of the electron field

Yes.

what about the excitation of the electromagnetic field?

That's usually called a photon. However, not all field states can be usefully decribed as "excitations" in this sense; i.e., not all field states can be usefully thought of as "particle" states.

Where does that manifest itself? Is it the static electric field that we always see?

No. A static electric field is one of those field states that can't be usefully thought of as a "particle" state.

the static electric "field" of the electron

Is not a state of the electron field. It's a state of the electromagnetic field (the one whose "particle" states are called photons).

So then it isn't a continuous field per se like the classical image of it.

The electron field, since it is a fermion field, does not have a "classical" counterpart. Only boson fields, like the electromagnetic field, have classical counterparts.

 

[PeterDonis]

It seems as if the constancy of c was originally attributed to a absolute universal undetectable "static field",

I don't know where you're getting this from. The constancy of c came from measurements of electromagnetic waves, which are not static.

It also seems that originally electrons were allocated individual fields

I don't know where you're getting this from either. Prior to QFT electrons were just thought of as particles; there was no field associated with them.

 

[FallenApple]

Please give a specific reference. This doesn't look right.

I think he explains it around 9:00 min. He draws a parabolid where the z axis is energy and the x and y-axis are fields. The contour is a circle which means the fields have to change value as one transverses it.

 

[PeterDonis]

He draws a parabolid where the z axis is energy and the x and y-axis are fields.

This has nothing to do with "creating charge". Charge is an inherent property of a field; more precisely, it's an inherent property of an interaction between fields--in the specific case of electric charge, it's the coupling constant of the interaction between the electromagnetic field and other fields (it can be different for different fields, since different fields can have different charges, but for any given field it's a constant).

 

[PeterDonis]

And that this charge happens at a contour of the energy function where the strength of the em field and the electron field are the inputs of the energy function.

No. What he's talking about here is a way of visualizing how oscillations in a field can "look like" particles. Basically, if the value of the field is at the bottom of the paraboloid, the field is in its ground state, also called the "vacuum" state, because in this state there are zero particles. But if the value of the field is somewhere up on the side of the paraboloid, then it is not in the ground state and you can (sometimes) view the state as a "particle". If the field has a charge (i.e., a coupling constant for interacting with the electromagnetic field), then the particle will be a charged particle; but the fact that the field's value in a "particle" state might be changing (for example, if the field's value is moving around in a circle at a constant "altitude" on the paraboloid, as Susskind describes it doing in a state of constant angular momentum) does not mean the charge (the coupling constant of the interaction with the electromagnetic field) is changing.

 

[FallenApple]

No. What he's talking about here is a way of visualizing how oscillations in a field can "look like" particles. Basically, if the value of the field is at the bottom of the paraboloid, the field is in its ground state, also called the "vacuum" state, because in this state there are zero particles. But if the value of the field is somewhere up on the side of the paraboloid, then it is not in the ground state and you can (sometimes) view the state as a "particle". If the field has a charge (i.e., a coupling constant for interacting with the electromagnetic field), then the particle will be a charged particle; but the fact that the field's value in a "particle" state might be changing (for example, if the field's value is moving around in a circle at a constant "altitude" on the paraboloid, as Susskind describes it doing in a state of constant angular momentum) does not mean the charge (the coupling constant of the interaction with the electromagnetic field) is changing.

What do you mean by we can sometimes see it as a particle? I thought particles are excitations in fields. So an excitation in fields can lead to other things besides particles? Would that be where the classical field comes from?

So the charge is the coupling constant and as a constant it doesn't change. So then if I have a charge at the value of energy E, then the charge can be of any combination of the EM field and the electron field? So basically there is no physical angular momentum since the view of the parabolid doesn't treat the horizontal variables as being parameterized by time.

 

[FallenApple]

Please give a specific reference. This doesn't look right.
Yes.
That's usually called a photon. However, not all field states can be usefully decribed as "excitations" in this sense; i.e., not all field states can be usefully thought of as "particle" states.
No. A static electric field is one of those field states that can't be usefully thought of as a "particle" state.
Is not a state of the electron field. It's a state of the electromagnetic field (the one whose "particle" states are called photons).
The electron field, since it is a fermion field, does not have a "classical" counterpart. Only boson fields, like the electromagnetic field, have classical counterparts.

So the static field is not a particle state and yet it has a strength so it is not of 0 value. I thought when fields reach non 0 values in QFT, we see particles.

So the electromagnetic field has a classical counterpart because it is made of bosons? Is it because of the pauli exclusion principle? Can I view the EM field as being made of descretized packets that can overlap smoothly to make a field because the pauli exclusion principle allows it?

 

[PeterDonis]

I thought particles are excitations in fields.

Yes, but not all states of quantum fields have a useful particle interpretation.

So an excitation in fields can lead to other things besides particles? Would that be where the classical field comes from?

The word "excitation" is usually used in connection with field states that have useful particle interpretations. But that's a matter of language, not physics. The physics, as I said before, is that not all quantum field states have useful particle interpretations. Quantum field states corresponding to classical static fields are among the states that don't have useful particle interpretations.

 

[PeterDonis]

I thought when fields reach non 0 values in QFT, we see particles.

That is not correct. See my previous comments.

So the electromagnetic field has a classical counterpart because it is made of bosons?

Because it is a bosonic field. That is not the same as being "made of bosons", because the latter language implies a particle interpretation, which, as I've said, states corresponding to classical static fields do not have.

Is it because of the pauli exclusion principle?

No. The Pauli exclusion principle only applies to fermions (or fermion fields, more generally).

Can I view the EM field as being made of descretized packets that can overlap smoothly to make a field because the pauli exclusion principle allows it?

No. See above.