# Why are particles in QFT assumed to be point-like?

1. Dec 28, 2015

### Ben Cooper

Why are particles in QFT assumed to be point-like?
This assumption is the source of ultraviolet divergences.
Does anyone know what is the source of this assumption, and what happens if you assume that particles are not point-like?

2. Dec 28, 2015

### bhobba

They aren't.

To be point-like position needs to be an observable:
http://www.mat.univie.ac.at/~neum/physfaq/topics/position.html

Wilson sorted out what's going on with ultraviolet divergences. Its because in QFT fields are modelled as a large number of blobs, QM is applied to those blobs, and the blob size taken to zero. Its taking the blob size to zero that is the problem. If you don't do that its modelled as having a cut-off in the theory. When you have that cut-off there is no divergences:

Thanks
Bill

3. Dec 28, 2015

### Demystifier

If you assume they are not pointlike, you loose simplicity. In particular, there are many inequivalent ways to make them not pointlike, so it's hard to know what (if any) is the correct way. Besides, most ways destroy some symmetries such as Lorentz symmetry.

4. Dec 28, 2015

### bhobba

How can they be point-like if position is not an observable eg photons?

Thanks
Bill

5. Dec 28, 2015

### Demystifier

In QFT, by "pontlike particle" one means states obtained by acting with a local field operator $\phi(x)$ on the vacuum.
For example, quark is a "pointlike particle" in a sense in which a proton (consisting of 3 quarks) is not a pointlike particle.

6. Dec 28, 2015

### bhobba

Yes - thanks for the clarification. Using that view I of course agree.

To the OP with that view of point-like its obvious nothing to do with divergences, the cause of which, and the solution of, these days is well known.

Thanks
Bill

7. Dec 28, 2015

### atyy

"Pointlike" is misleading terminology - it just means a quantum particle not made of more fundamental quantum particles.

The pointlike assumption does not necessarily lead to ultraviolet divergences. An example of a QFT in which the pointlike assumption does not lead to ultraviolet divergences is the theory of the free electron field. It is also believed, but not proven, that QCD does not have ultraviolet divergences even though it contains quarks, which are pointlike particles.

When the pointlike assumption does lead to ultraviolet divergences, then it is assumed that the pointlike particles are not truly pointlike, and are in fact "made of" more fundamental particles or strings. An example of such a theory is the theory of the graviton as a pointlike particle. We don't know for sure that it necessarily has ultarviolet divergences, but most informal calculations suggest that it does. String theory tries to remove the ultraviolet divergences by saying that the graviton is not pointlike, but a vibration of a string.

8. Dec 29, 2015

### Ben Cooper

Thank you all for all these answers.
I need to study this issue more closely before I can establish a solid opinion on that subject.
When I feel I have a full understanding of that problem, I'll respond to everything said here.
This discussion is far from over, I think there is way more to particles then just points...

9. Dec 29, 2015

### atyy

But I hope you got the basic message: point particles don't always cause ultraviolet divergences, but when they do - you are right - the point particle assumption is generally thought to wrong, and particle are not just points.

10. Dec 29, 2015

### Islam Hassan

I assume it is possible to have a description of nature (ie QFT) based on a certain model (ie point-like particles) which gives very accurate predictions up to a certain scale but which is erroneous beyond that.

For example, if string theory is true, then QFT would remain valid at the energy scales we can presently measure but this predictive validity would be based on the false premise of point-like particles. Am I making sense here?

IH

11. Dec 29, 2015

### A. Neumaier

Such assumptions are matters of scale. Even really big objects such as stars are pointlike particles when viewed from far enough away.

12. Dec 30, 2015

Yes.