= Polarization in geometric quantization
{title2=$\mathcal F\subset T_{\mathbb C}P$}
= Geometric quantization polarization
{synonym}
A polarization is an involutive complex rank-half distribution on which the <symplectic form> vanishes. Polarized prequantum sections satisfy $\nabla_Xs=0$ for $X\in\mathcal F$. A real polarization is tangent to a <Lagrangian foliation>; a complex <Kähler> polarization uses the antiholomorphic tangent spaces. Only observables whose <Hamiltonian flows> preserve the chosen distribution act directly on the polarized space. Singular leaves, <holonomy> and changes of polarization are genuine quantization difficulties.
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