In geometric quantization, the choice of polarization, has been regarded as "additional" choices in the construction. We will discuss the hypothesis that the choice of a pair of transverse polarizations can be interpreted as Poincare-Birkhoff-Witt isomorphisms. In particular, we will show how for symplectic vector spaces, there is an irreducible representation of the Heisenberg Lie algebra for every such choice. This construction unifies the families of representations of the Heisenberg Lie algebra constructed by Satake, Grossmann, and Lion-Vergne.