# B Shape of elementary particles in QFT, etc?

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1. Aug 10, 2016

### icantevenn

Hello,
I hope this is not a stupid question as I am not a physicist. But I was curious about how contenders for the so-called Theory of Everything view the shape of the elementary particles. I know that the basic idea of string theory is related to the shape of elementary particles as one dimensional, as opposed to zero-dimensions of classical mechanics, to include Quantum Theory. I am curious what is the shape of elementary particles in other theories that seek to unify QT and GR, such as Quantum Field Theory?
Thanks.

2. Aug 10, 2016

### ShayanJ

Quantum Field Theory (QFT) doesn't unify QT and GR, it applies the framework of QT to classical special relativistic field theories.
In QFT, particles are assumed to be point-like.

3. Aug 11, 2016

### bhobba

That's true, but just to flesh it out a bit more.

For GR see:
https://arxiv.org/abs/1209.3511

And what a particle is in QFT is a bit more nuanced - its analious to whats happening in the quantum treatment of the harmonic oscillator:
http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Thanks
Bill

4. Aug 11, 2016

### icantevenn

I guess I used the wrong word. What I meant, I realise, is Quantum Gravity and not QFT.

5. Aug 11, 2016

### bluecap

Just read the above paper, interesting. Is it possible the electron fields are subject to interpretations too like the wave function in QM where the electron fields can also be real like Bohmian?

6. Aug 11, 2016

### Demystifier

It's possible:
http://arxiv.org/abs/quant-ph/0302152

7. Aug 11, 2016

### bluecap

If fields are considered as beables (i.e. elements of reality) then an appropriate detector can be constructed that should be able to detect such fields? But the fields are everywhere, it should be able to detect them like the microwave background radiation?

8. Aug 11, 2016

### Demystifier

Even in classical field theory you detect not fields as such but field variations.

9. Aug 11, 2016

### bluecap

Can the theoretical bohmian quantum fields also have field variations?
The microwave background radiation was discovered accidentally.
What kinds of setups can theoretically detect these bohmian quantum fields variations?

10. Aug 11, 2016

### Demystifier

How do you detect light from the bulb?

11. Aug 11, 2016

### bluecap

The electromagnetic field is real in QED.. but in electron or quark matter fields.. they are not beables in orthodox QFT.. so are you saying the bohmian electron field can be detected by bohmian electron field detector? What kind of detector can differentiate between electromagnetic field and bohmian electron, quark fields?

12. Aug 11, 2016

### bhobba

Just to elaborate the reason classical fields are considered 'real' is because they carry energy and momentum. Things are more 'obscure' in QFT because the fields are quantum operators which are rather mathematical to begin with. The 'realty', if such exists are like to be with the Fock space thee operators act on.

Thanks
Bill

13. Aug 11, 2016

### bhobba

Again its reality is an interpretational issue. Classically its real - but in QFT its much more complicated.

Thanks
Bill

14. Aug 11, 2016

### Demystifier

Electromagnetic field is not a beable in orthodox QFT.

15. Aug 11, 2016

### anorlunda

That is what I was taught. But another recent thread pointed me to "transversely shaped photons" and to Bessel beams as an example of how to shape them.

I don't understand. Point-like photons and shaped photons sounds like a contradiction. What gives?

16. Aug 11, 2016

### Demystifier

Photons are pointlike, while the shape is the shape of the wave function. One should distinguish the photon from its wave function.

17. Aug 11, 2016

### bluecap

So since the quantum fields in Bohmian QFT is a beable.. and this is supposed to be really there.. so what kind of instruments can theoretically image Bohmian electron fields for example? For bohmians particles. We can see them with our own eyes.

18. Aug 11, 2016

Staff Emeritus
This thread is kind of drifting.

I think the OP needs to clearly specify what he means by "shape". What measurements would one make to determine "shape". Only then can we discuss what theoretical predictions are with any confidence. For example, for a charged particle, one might ask if the electric field lines are identical to what is produced from a small charged sphere or whether and how they deviate.

19. Aug 11, 2016

### bhobba

You are missing a key point.

BM has been deliberately cooked up to be indistinguishable from standard QM so there is no way to do what you suggest.

There was a bit of interest in doing that a while ago eg:
http://arxiv.org/abs/quant-ph/0206196

However it soon became apparent it was incorrect. When you think about it it must be the case as it reduces to standard QM there is unlikely any way to tell the the difference.

Thanks
Bill

20. Aug 12, 2016

### A. Neumaier

A compass routinely detects the direction of the magnetic field itself not only deviations.
A point particle is a particle responding to an external electromagnetic field like a classical point charge. Point-like means it is almost that - the e/m form factor deviates from it only through corrections by other fields. Thus being pointlike or not is a property of the particle species just like mass, charge, or spin.

The shape of a particle is, in contrast, a property of the state of the particle just like mean position (if it exists), mean momentum etc. Hence it depends on the particular electron, photon etc. you are considering. It is given in the Heisenberg picture by $\psi^*E(x)\psi$ where $E(x)$ is the relativistic energy density operator. The geometric shape is obtained as the set of $x$ where this is significant - similarly to how one speaks of the shape of a cloud or the corona of the sun.