# I Renormalisation and the Landau pole

1. May 6, 2017

In the B level thread:......"how to change electron and proton charge".........it was claimed that "the closer you get to an electron the bigger the charge".

This struck me as odd because I though that electron charge was a fundamental constant and so I asked for clarification. This was given but extra advice was that to pursue the matter further goes beyond B level and into A level. So it would be best to start a new thread. Here it is.

My initial question refers to a wiki article which was referred to. Amongst other things the article states:

"For example in QED, an electron appears to be composed of electrons, positrons and photons as one views it at higher resolutions at very short distances".

I don't get it. How can an electron be composed of electrons? And how can it be composed of positrons or photons? Taken literally the sentence can be interpreted as an electron (singular) being composed of all three particles simultaneously.

I think I know what is meant by higher resolutions but what is meant by "very short distances"? Does it mean very small particle separations?

It's a quite lengthy article but I can't get anything from it because I can't even get beyond the single statement above. I have spent quite a bit of time searching elsewhere but have found nothing suitable as yet.

The main thing I would like to know is...... does the charge really have different values in different situations? Or is there such a thing as an effective charge which is analogous to effective mass?
Thank you

2. May 6, 2017

### ftr

3. May 6, 2017

Thank you ftr. I think I'm getting the gist of it but one thing that confuses me are the equations for the Uehling potential from the wiki page that you referred to. Look at the second equation for example. It doesn't seem to balance dimensionally. Also, e is raised to a power of negative 2mer. Shouldn't the power factor (2mer) be dimensionless also? I guess I might be overlooking something.
Thank you.

4. May 6, 2017

### ftr

The units used is similar to natural units, m units is inverse length so mr is dimensionless. you end up with energy(V) =inverse length=1/r

5. May 6, 2017

Thanks ftr. I thought it was something like that. Natural units is yet another thing I need to brush up on.

6. May 6, 2017

### ftr

You are welcome. Natural units simplify equations and make the physics a bit more clear.

7. May 6, 2017

### bhobba

The links FTR gave, and the links in those link basically tells you all that can be said at the B or even the I level.

Now you know all about it - well at the appropriate level anyway. There is MUCH more to say at an advanced level such as its even possible to do QED without renormalisation and infinities but enough said for now.

Almost forgot here is a good book at the B level on it:
https://www.amazon.com/Infinity-Puzzle-personalities-politics-extraordinary-ebook/dp/B005ZEV4OC

I have a copy and can vouch for how good it is.

Thanks
Bill

Last edited by a moderator: May 8, 2017
8. May 6, 2017

### atyy

It is not the same electron. It is like saying if you take a circuit with many resistors, you can model it as an effective circuit with one resistor.

Thevenin's theorem: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html

Using the circuit analogy for renormalization, if you look at the circuit with high resolution, you will see many resistors. If you look at the circuit with low resolution, using Thevenin's theorem, you will see one resistor.

Renormalization is the process of getting the low resolution view from a high resolution view. Experiments at the LHC are relatively low resolution.

We can also try to run renormalization in the "backwards direction" from low resolution to high resolution. The Landau pole problem is that it is not possible to run renormalization from low resolution to perfect infinite resolution. It is not a problem for our low resolution experiments, but it says either our theories are incomplete (maybe needing strings) or that our process of renormalization to high resolution is too simple minded (asymptotic safety).

Last edited: May 6, 2017
9. May 7, 2017

### A. Neumaier

The electrons talked about are effective electrons. Unlike properties of the electron field, which is a fundamental concept, electrons as particles are approximations obtained by recasting the fundamental theory into an easier accessible effective theory.

All properties of particles in an effective theory depend on the time/space/energy scale for which the effective theory was derived.

Higher energies = shorter times = shorter distances. The conventional, macroscopic electron is the one at macroscopic times and distances = very low energies.

Last edited: May 7, 2017
10. May 7, 2017

### A. Neumaier

You should change the title of the thread to ''Electrons at very short distances'' - your question has nothing to do with the Landau pole.

11. May 7, 2017

Thanks everyone. I think I've got the general idea. I hope now to get a rough idea of how the classical Coulomb potential depends on factors such as particle separation. I have been doing some searches on this and found an approximate equation in the wiki article on Lamb shift. According to the article the potential is not proportional to 1/r but proportional to 1/( r+dr). Apparently the dr is referred to as a perturbation. I'm assuming that dr becomes appreciable for for atomic sizes of the order of 10 to power minus eleven metres, or thereabouts, but what is an approximate value of dr?
Thank you.

12. May 7, 2017

### ftr

But by your own standpoint on vacuum it seems what you call effective is really fundamental and what you call fundamental is approximate since there is no such as noninteracting.

13. May 7, 2017

### A. Neumaier

No. Fundamental means (at the present state of knowledge) the standard model.

It defines (by the usual standards of theoretical physics) the meaning of the terms, in particular of an (interacting) electron field and of the unique interacting vacuum state. It defines particles only in their noninteracting, asymptotic incarnation - i.e., in practice the input and output of scattering experiments.

To turn these into particles at finite times you need to make quite some approximations, and in particular choose an energy scale for which these approximations should be reasonably good. Then the particles become effective particles.

14. May 7, 2017

### ftr

Of course, I understand the STANDARD MODEL. But I like my particles the way they are.

15. May 7, 2017

### A. Neumaier

But the way they are depends on how they are effectively defined. They are slightly different things depending on the context (i.e.., the energy scale of interest).

Last edited: May 7, 2017
16. May 8, 2017

### vanhees71

Yes, and to the dismay of many HEP physicists the particles behave with pretty good accuracy as the Standard Model predicts. Last summer all the candidates (evidences below the $5 \sigma$-significance level) were ruled out. Recently there's a new candidate from LHCb, and we'll see whether this finally survives as physics beyond the SM or not. That's how science works!

17. May 8, 2017

### ftr

I think my comment was misunderstood by Arnold and you. I do agree with the SM, but my comment was philosophical in the sense that which picture of the electron was fundamental, mine is that the effective seems more fundamental i.e. the electron is as SOMETHING emitting/absorbing the "virtual particles".

18. May 8, 2017

### ftr

19. May 8, 2017

### A. Neumaier

But all the talk about virtual particle requires quantum field theory to relate it to formulas and predictions. Thus QFT (i.e., the electron field) is fundamental, while the ''something'' is only a heuristic to talk intuitively about certain aspects of the fields. How can that be fundamental???

20. May 8, 2017

### vanhees71

If this is philosophical, I get further confirmation for my aversion against philosophy (SCNR).