Generalized Euler angle parameterization for U(N) with applications to SU(N) coset volume measures

In a previous paper [J. Phys. A: Math. Gen. 35 (2002) 10467] an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CPN as well as other SU(N) and U(N) cosets, normalized to this parameterization, will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived. (C) 2004 Elsevier B.V. All rights reserved.