= Geometric quantization
Geometric quantization associates quantum states and observables with a <symplectic manifold>. A first step uses a complex <line bundle> with a <connection on a vector bundle> whose curvature is proportional to the <symplectic form> divided by $\hbar$; its existence imposes an integrality condition. A real polarization is an integrable half-dimensional distribution with <Lagrangian submanifolds> as leaves. Requiring sections to be covariantly constant along the leaves reduces the variables to a configuration-space description. Restricting the curvature to a Lagrangian leaf gives zero, permitting local flat sections; global sections can require trivial holonomy. Exact Lagrangian graphs also describe local semiclassical phases through their generating functions.
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