coadjoint action of elements in $\operatorname{SU}(2)$ amounts to rotating the *Bloch vector* $\vec r$ via the two-fold covering map $\operatorname{SU}(2) \rightarrow \operatorname{SO}(3)$. Therefore, coadjoint orbits are spheres, commonly called *Bloch spheres* in quantum mechanics. They can be labeled by their radius $r$, that is, by their intersection with the positive half of the $z$-axis. Points on such a sphere correspond to Hermitian matrices with eigenvalue spectrum $(\frac {1+r} 2, \frac {1-r} 2)$. Note that $\rho(\vec r)$ is positive-semidefinite (i.e., a density matrix) if and only if $\vec r$ is contained in the unit ball of ${\mathbb R}^3$.

The non-Abelian moment map is just the inclusion map of a Bloch sphere into ${\mathbb R}^3$. Hence its composition with the quotient map $\tau_{\operatorname{SU}(2)}$ sends all points in a Bloch sphere of radius $r > 0$ to $r$, while the Abelian moment map projects all points onto the $z$-axis. The Liouville measure is equal to the usual round measure, normalized to total volume $r$. Therefore, the non-Abelian Duistermaat–Heckman measure of a Bloch sphere with radius $r$ is equal to the Dirac measure $\delta_r$, while the Abelian Duistermaat–Heckman measure is obtained by pushing forward the Liouville measure onto the $z$-axis (see ). As already 