QCD

QCD as a Non-Abelian Gauge Theory

  1. SU(3) Transformations
    Consider a three component vector. Any SU(3) transformation U acting on such a vector can be written as
    su3transformation
    where αj are real numbers (rotation angles) and λj are hermitian matrices.

    Since U is a SU(3) transformation (det U=1) the λj are traceless:
    traceless
    There are only eight linearly independent traceless 3x3 matrices.
    A possible choice are the Gell-Mann matrices:
    gellmanmatrices

    The λj are forming an algebra:
    lambdaalgebra
    with the total antisymmetric structure constants fjkl
    fjkl
    An infinitesimal SU(3) transformation is given by:
    infinitesimalsu3transformation

  2. Local SU(3)C Transformations
  3. Quark-Gluon Coupling
  4. Colour Singlet, Nuclear Forces