The problem of quantizing a symplectic manifold (M,��) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,��) is the space of (Bcc,B') strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M, and the choice of ��is encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2,R). Another application is to Chern-Simons gauge theory.

70 pp, v2: references added