Generalized Euler Angle Paramterization for SU(N)

Abstract

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.

36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Gen