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Gluons, where do they come from and where do they go?

by llynne
Tags: gluons, nuclear composition
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Jan27-14, 07:47 AM
P: 1,058
As I said, it was a recommendation rather than an offence (I didn't call you stupid or anything- i don't believe in such a thing in the first place). Just a way for both sides to understand what each other is speaking about.
In the mathematical procedure, gluons appear because strong interactions can be described as a local SU(3) gauge theory.
So let's start from the analogy of the electromagnetic field. The electromagnetic field comes when you impose local U(1) gauge invariance. In general a U(1) transformation will be:
[itex] Φ\leftharpoondown e^{iYa(x)}Φ [/itex]
If you put the transformed expression into the lagrangian, you will see that it's not invariant as it is... The kinetic term:
[itex] L=∂_{μ}Φ ∂^{μ}Φ^{*}[/itex]
will give you an extra term containing the partical derivative of [itex]a(x)[/itex] since it's a local transformation and thus depends on spacetime [itex]x[/itex] (i denote [itex]x^{μ}[/itex] as just [itex]x[/itex] here). Nevermind, to avoid the whole maths, you will have to introduce a new field to keep the invariance, which in fact will change your partial derivative to covariant derivative... Furthermore new interactive terms will be allowed for your local U(1) transformation invariance (the term will correspond to the "electromagnetic" field).

If you do the same for SU(3) (by keeping in mind it's not an abelian group) you will get also another field that will correspond to its interaction with itself. That'll be the field of gluons.

Again it's a model (QCD) that works nicely in explaining what we see, and that's why we have it. For example it was at the first stages of studying nuclear forces that physicists put in action the String Theory. Of course (since it's a fact now) QCD dropped it out.
The problem is that at low energies, the coupling constant of QCD is not working perturbatively because it is too big to give any reasonable result (higher orders will be more important and stuff). In that region, someone uses effective theories like mesons. The energies of nuclei (~MeV) are in that region, so it would make no sense to use gluons as medians of interaction and uses the pion mesons interchanging models. At the energies of a proton (~1GeV) or more, QCD is a good perturbative theory (it works).
Jan27-14, 09:51 AM
Drakkith's Avatar
P: 12,014
Quote Quote by llynne View Post
I'm sure I read it, not sure what remains in my brain. I read about chirality several times but if I ask myself what it is, I find nothing. But I know how my brain works. I take in information and suddenly it comes together. I found myself asking isn't what a gluon does more like a field? Not really trying to display my ignorance but for a quick way to find if that has already been worked through.
Have you looking into what quantum field theories are?
Here's a link if you haven't.
Jan28-14, 06:55 AM
llynne's Avatar
P: 27
I appreciate all the help. I am off to read field theories with a bit more of an idea of what it is about.
Jan28-14, 11:33 AM
P: 1,058
You can find interesting sites (lecture notes) from where you can suck knowledge concerning QFT. Also from books (chronological order):
Bogoliubov & Shirkov- introduction to the theory of quantized fields (1959)
Bjorken & Drell- relativistic quantum mechanics (1964)
Cheng & Li- Gauge theories of elementary particle physics (1984)
Peskin & Schroeder- An introduction to Quantum field theory (1995)
Weinberg- The quantum theory of fields (1995)
Ryder- Quantum field theory (1996)

From them, you can have your own look and choose which fits in your needs and stuff... :)
Bjorken and Drell are just a good introduction to let you think and I don't think they formulate the QFT in the normal formalism (with the Lagrangians and stuff), but it's still nice and helped me a lot.
Also I was personally helped by Schroeder and Peskin and by Cheng and Li...
Jan28-14, 04:21 PM
llynne's Avatar
P: 27
Thanks very much, that's a very helpful list..

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