Generalized twistors and geometric quantization

The curved phase space $M$ of an arbitrary generalized Hamiltonian system that possesses invariance with respect to a Lie group $G$ is considered. The geometric and BRST quantizations of these phase spaces are considered. For $M$ the space of universal ghosts (specters) $S$ is introduced; it contains the space of ghosts $D$ for any admissible Lie group $G$ of constraints. The phase manifold $M$ is embedded in the manifold of generalized twistors $Z$. A quantization scheme that generalizes the approaches of the geometric and BRST quantizations is described. In this scheme, the quantum theory is formulated in terms of the generalized twistor manifold and bundles over it.