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

by llynne
Tags: gluons, nuclear composition
 P: 916 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: $Φ\leftharpoondown e^{iYa(x)}Φ$ If you put the transformed expression into the lagrangian, you will see that it's not invariant as it is... The kinetic term: $L=∂_{μ}Φ ∂^{μ}Φ^{*}$ will give you an extra term containing the partical derivative of $a(x)$ since it's a local transformation and thus depends on spacetime $x$ (i denote $x^{μ}$ as just $x$ 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).