On the geometric quantization of Jacobi manifolds

Abstract

The geometric quantization of Jacobi manifolds is discussed. A natural cohomology (termed Lichnerowicz–Jacobi) on a Jacobi manifold is introduced, and using it the existence of prequantization bundles is characterized. To do this, a notion of contravariant derivatives is used, in such a way that the procedure developed by Vaisman for Poisson manifolds is naturally extended. A notion of polarization is discussed and the quantization problem is studied. The existence of prequantization representations is also considered.