QCD

QCD as a Non-Abelian Gauge Theory

  1. SU(3) Transformations
  2. Local SU(3)C Transformations
  3. Quark-Gluon Coupling
    To study the coupling between quarks and gluons the full Dirac equation in QCD is written as follows:
    qcddiracequation
    That is, a state χC with colour C couples to the gluon field with the strength gs and changes to another colour charge C'. mediated by λjGjμ.

    This operator can be rewritten:
    lambdajgj
    The operators I+-, U+- and V+- are ladder operators changing the colours of the quarks. This is depicted in
    ladderoperators
    EXAMPLE 1: The transition from a quark with colour charge G to a quark with colour charge R is depicted in
    colourtransition
    where the net colour charge is conserved at the vertex by radiating a gluon with colour charge (G anti-R).

    EXAMPLE 2: There are also transitions without colour change. They are mediated by the gluon fields:
    g3g8
    with the corresponding matrices λ3 and λ8.

    The gluons carry colour charges, more precisely a colour and an anti-colour. The gluon states can be constructed by forming the direct product of a SU(3)C triplet and SU(3)C anti-triplet as depicted in
    colouroctet
    As a result one obtains a colour octect plus a colour singlet.

  4. Colour Singlet, Nuclear Forces