  We construct a dynamical quantization for contact manifolds in terms of a
flat connection acting on a Hilbert tractor bundle. We show that this contact
quantization, which is independent of the choice of contact form, can be
obtained by quantizing the Reeb dynamics of an ambient strict contact manifold
equivariantly with respect to an R+-action. The contact quantization further
determines a certain contact tractor connection whose parallel sections
determine a distinguished choice of Reeb dynamics and their quantization. This
relationship relies on tractor constructions from parabolic geometries and
mirrors the tight relationship between Einstein metrics and conformal
geometries. Finally, we construct in detail the dynamical quantization of the
unique tight contact structure on the 3-sphere, where the Holstein-Primakoff
transformation makes a surprising appearance.
