Differential geometry on SU(3) with applications to three state systems

This is the authors' abstract. We don't add key points for this paper.

The left and right invariant vector fields are calculated in an “Euler angle”-type parametrization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This enables the calculation of the invariant volume element or Haar measure. These are then used to describe the density matrix of a pure state and geometric phases for three state systems.