Types of quantum field thories
A symplectic manifold serves as the target space for the 2-dimensional sigma-model TQFT called the A-model. If the symplectic manifold arises as the complexification of a phase space of some physical system, then one finds that the boundary path integral of the A-model on cosiotropic branes computes the path integral and the geometric quantization of this physical system.
The main original article is
A relation to the path integral is discussed in