Perhaps this is pretty basic, but somehow I'm not getting it:
Given a symplectic manifold $(M,\omega)$, a Hermitian line bundle $B \rightarrow M$, pick a symplectic frame and set $$ \theta = \frac{1}{2} (p_adq^a-q^a dp_a),$$ which is a symplectic potential.
I've read, that $\theta$ determines a local trivialization, in which the sections of $B$ can be represented by complex functions, depending on $p,q$.
The question is: How does $\theta$ (or perhaps more general, any canonical 1-form) determine the trivializations of a vector bundle?
Also, about "(...)in which the sections of $B$ can be represented by complex functions, depending on $p,q$.": Does this mean that one can equivalently work with the composition of a loc. triv. and a section, instead of the section itself? I thought that one could intuitively view the sections in the Hermitian line bundle locally as complex-valued functions. Is the 'locally'-part where the triv. comes into play?