Invariant Measures and Volumes on SU(N) and its Complex Projective Cosets A Fully Analytic Treatment

A fully analytic treatment of the invariant (Haar) measures and volumes on the special unitary groups SU(N) and on their complex projective cosets. The measure is constructed from the fibration and the cascade of odd spheres, with every step displayed: the Jacobian of the parametrisation, the recursion for the measure, and the closed form for the volume of SU(N) and of the projective quotients. The results are compared with the classical formulas of Marinov, including his published correction, and the conventions under which each volume is quoted are stated explicitly.