I recently encountered a formula that fell a little bit from the sky:
Given: A symplectic manifold $(M,\omega)$, a Hermitian line bundle $\pi:B\rightarrow M$, a connection $\nabla$ on $B$ and a symplectic potential $\theta$ (where $d\theta = \omega$), it holds that \begin{equation} \nabla s_1 = -i\theta s_1, \end{equation} where $s_1$ stands for the frame of $B$ (so that, for any section $s\in\Gamma(B)$ it is possible to express $s$ as $s= fs_1$, with $f:M\rightarrow \mathbb{C}$ a complex function.
How can one derive the above equation for the connection? What's the background?