# I QFT fields Real or not?

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1. Nov 18, 2016

### ftr

Sorry, I know this has been talked about many times before but I like to put the question in a direct way so I may understand.

Since there are more than 10^80 particles and radiation, how can a single point in space carry the values for all these fields at the SAME time all the time if they are real/intrinsic(i.e. not effective like classical variables like pressure, temperature).

2. Nov 18, 2016

### Demystifier

If you think that each of the $10^{80}$ particles has its own field, then you are wrong. Independent of the number of particles in the Universe, there is only about 20 different kinds of fields.

That being said, it is not known whether these 20-or-so fields are effective or fundamental ("real").

Last edited: Nov 18, 2016
3. Nov 18, 2016

### A. Neumaier

On the fundamental level, there are according to present knowledge only 6 fields - the lepton field, the quark field, the gluon field, the electroweak field, the Higgs field, and the gravitational field, each with a fairly large (but compared to the baryon number of the universe exceedingly small) number of components.

On the level of everyday experience there are many more fields - for example, each fluid has its own field.

Last edited: Nov 18, 2016
4. Nov 18, 2016

### Demystifier

There are several different ways of counting. I like to count components with different mass as different fields.

But if you want to split hairs, if electroweak SU(2)xU(1) field is counted as one field, then gluo-electroweak SU(3)xSU(2)xU(1) field can also be counted as one field.

And by the way, you forgot Higgs.

Last edited: Nov 18, 2016
5. Nov 18, 2016

### A. Neumaier

But this is unnatural since there is mass mixing. There is no reason to prefer the mass basis over any other basis.
No, it is you who are splitting - not hairs but fields!!!
But one cannot naturally split the electroweak field into an SU(2) field and an U(1) field as these have no independent meaning - the electromagnetic U(1) is the diagonal of the SU(2)xU(1)!
On the other hand, if one wants to unsplit hairs as you suggest, one should put all fields into one big field with many components.
Yes, corrected. I think of it as the scalar part of the gravitational field, but this is not the accepted usage.

6. Nov 18, 2016

### ftr

Thanks both.

So does the lepton field exist inside the proton? what are they doing there, when their values possible change to indicate an electron has materialized and how does the proton then behave, it certainly has a strong charge?

Moreover, isn't the wavefunction should cover all of spacetime even at extremely low probability?

7. Nov 18, 2016

### Staff: Mentor

A field is defined to be something that has a value (not necessarily a number - there are vector and tensor fields) at every point in spacetime, so the lepton field has a value everywhere, including "inside a proton".

The quotes around the words "inside a proton" are there because none of these particles that we're talking about are little tiny balls with an inside and an outside.

8. Nov 19, 2016

### A. Neumaier

Yes, strictly speaking, all fields are everywhere in space and time, but one can neglect them where the field strength is too tiny.

For a proton inside a hydrogen atom in the ground state the lepton field even has its maximal density at the center of the proton!

On the level of quantum chemistry (systems of nuclei and electrons), electrons are conserved, hence they cannot materialize but have to flow. Macroscopically, this is seen as the flow of electricity in the electromagnetic field. Microscopically, the lepton (electron) field accounts for such things as delocalization, smearing out the electrons. The pointlike picture is adequate only in electron beams.

9. Nov 19, 2016

### ftr

can you give a reference please, thanks.

10. Nov 19, 2016

### ftr

So my question again, how is it that a single point(unless it is a world by itself) carries all these fields of scalar, vector , tensor ... this is like superposition running really wild. On top of that the good old mysterious CC, and at a point where a quark or an electron exists all these fields are jamming.

11. Nov 19, 2016

### Staff: Mentor

The same way it "carries" the classical electrical, magnetic, and gravitational fields - those are vector fields, and there's no problem saying that all three can have values at the same point.

12. Nov 19, 2016

Staff Emeritus
Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...

13. Nov 19, 2016

### ftr

My understanding is that these are classical and not fundamental like QM picture(suppose to be).

14. Nov 19, 2016

### ftr

I am not sure what you are refering to. Hydrogen model is handled by plain QM, there is no talk of "fields".

15. Nov 19, 2016

### Staff: Mentor

What you're calling "plain QM" is quantum field theory with the simplifying assumptions that the energy is low enough that the particle numbers are fixed and that the speeds involved are small compared with the speed of light. And I am at a loss to understand how you can say "there is no talk of fields" there when the entire problem and its solution are expressed in terms of functions of position.

16. Nov 19, 2016

### ftr

What I meant is that standard QM books do not use QFT to solve the hydrogen atom problem.

17. Nov 19, 2016

### vanhees71

For a modern solution of the hydrogen problem in QED, see

S. Weinberg, Quantum Theory of Fields, Vol. 1

18. Nov 19, 2016

### ftr

Ok thanks I will , I have all three volumes but I only see Dirac equation being solved with radiative corrections.

19. Nov 20, 2016

### A. Neumaier

In the present situation of a single electron, the field strength is proportional to the spatially probability density, which is calculated in many textbooks. For the ground state it is spherically symmetric and decays exactly exponentially with the distance from the center, hence is maximal there.

20. Nov 20, 2016

### A. Neumaier

The field is everywhere, not just at a single point. To translate from the QM particle picture to the (more accurate and more basic) QFT picture you need to rewrite things in terms of second quantization language (which is quantum field theory) and evaluate the expectation of the charge density operator at an arbitrary point $x$ in the ground state of a single hydrogen atom. This is a very useful exercise.