Differential Geometry on SU(3) with Applications to Three State Systems
Mathematical Physics
2009-10-31 v1 math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.math-ph/9807032,
title = {Differential Geometry on SU(3) with Applications to Three State Systems},
author = {Mark Byrd},
journal= {arXiv preprint arXiv:math-ph/9807032},
year = {2009}
}
Comments
17 pages, LaTeX2e, Accepted by J. Math. Phys