QCD

QCD as a Non-Abelian Gauge Theory

1. SU(3) Transformations
   
2. Local SU(3)_C Transformations
   
3. Quark-Gluon Coupling
   
4. Colour Singlet, Nuclear Forces
   
   COLOUR SINGLET GLUONS
   
   Let's consider the colour singlet gluon g_sing: This type of gluon is not realized in nature. The reasoning is:
   * Hadrons are colour singlets.
   * If hadrons exchanged g_sing nuclear forces would have infinite range in contrast to the observed typical range of O(1 fm).
   
   For that reason one considers local SU(3)_C transformations instead of local U(3)_C transformations.
   
   
   NUCLEAR FORCES
   
   Nuclear forces can not be mediated by one-gluon exchange as can be seen as follows.
   Consider a transition where a hadron H radiates colour-octet gluon: H -> H' + gluon.
   H' is required to be a colour singlet. To guarantee this the radiated gluon needs to be at least a colour neutral gluon, that is, g₃ or g₈.
   
   However, one is free to apply a SU(3)_C transformation to g₃ or g₈. As a consequence, the gluon carries a colour charge and hence the hadron H' as well.
   
   
   That is, nuclear forces has to be considered as effective forces mediated by multi-gluon exchange leading to a short-range force although gluons themselves are massless.
   
   The analog situation in QED is the effective Van-der Waals force (proportional to r^-7) due to multi-photon exchange.