Differential Geometry on SU(3) with Applications to Three State Systems
arXiv:math-ph/9807032 · doi:10.1063/1.532618
Abstract
The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization 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.
17 pages, LaTeX2e, Accepted by J. Math. Phys