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

Abstract

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.