= Prequantum line bundle
{title2=$F_\nabla=i\omega/\hbar$}
A <prequantum line bundle> is a Hermitian <line bundle> over a <symplectic manifold> with unitary <connection on a vector bundle> of the displayed curvature. With $\omega=-d\theta$, a local connection is $\nabla=d-i\theta/\hbar$. Reversing the Hamiltonian-vector-field convention or passing to the dual <line bundle> reverses the corresponding curvature convention. Integrality of $\omega/(2\pi\hbar)$ on closed two-cycles is the topological existence condition.
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