= Unitary moment map of an isotropic oscillator
{title2=$\mu_A=z^\dagger A z,\quad z=(x+ip)/\sqrt2$}
On the canonical <cotangent bundle> $T^*\mathbb R^n$, $\omega=i\sum dz_j\wedge d\bar z_j$ and $H=z^\dagger z$. The <unitary group> acts by $z\mapsto Uz$, preserving both. For a Hermitian $A$, the generator $-iA$ has Hamiltonian $\mu_A=z^\dagger Az$. The <Poisson bracket> satisfies $\{\mu_A,\mu_B\}=\mu_{-i[A,B]}$, with no central term. The central generator has moment map $H$; imaginary antisymmetric matrices give ordinary <angular momentum>, while real symmetric matrices give quadratic observables mixing position and momentum.
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