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 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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- November 1998
- DOI:
- 10.1063/1.532618
- arXiv:
- arXiv:math-ph/9807032
- Bibcode:
- 1998JMP....39.6125B
- Keywords:
-
- 02.40.Hw;
- 21.60.Fw;
- 11.30.Hv;
- 12.38.-t;
- 02.20.Sv;
- Classical differential geometry;
- Models based on group theory;
- Flavor symmetries;
- Quantum chromodynamics;
- Lie algebras of Lie groups;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 17 pages, LaTeX2e, Accepted by J. Math. Phys