## Abstract

The problem of quantizing a symplectic manifold (M,ω) 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,ω) is the space of (B_{cc}, B^{1}) strings, where B^{cc} and B^{1} are two A-branes; B^{1} is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B^{1} is supported on M, and the choice of ω is encoded in the choice of B^{cc}. As an example, we describe from this point of view the representations of the group SL(2, R{double-struck}). Another application is to Chern-Simons gauge theory.

Original language | English (US) |
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Pages (from-to) | 1445-1518 |

Number of pages | 74 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 13 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2009 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)