Quantum Space, Strings and the Gravitization of the Quantum

In the study of purely quantum phenomena, such as occur in double slit experiments, etc., it is useful to introduce modular variables rather than the more familiar positions and momenta. I will first review these variables and then show how they may be understood on a mathematical level as a generalization of geometric quantization. Playing a central role here is the Heisenberg group and its commutative subgroups. Our usual notion of classical space can be identified with a particular choice of commutative subgroup corresponding to a classical Lagrangian subspace of phase space, that is a choice of classical polarization. There are however purely quantum polarizations that correspond to a choice of modular variables. Such quantizations generically involve a dimensional scale in addition to \hbar. In simple quantum systems, the scale is set contextually, for example by a slit spacing.  A new notion of quantum space(time) emerges if we suppose instead that the scale is fundamental. I will provide substantial evidence that, contrary to the textbook accounts, this mechanism is present in ordinary string theory. Thus string theory describes an inherently quantum gravitational theory, for which the usual string constructions correspond to certain semi-classical limits with a local space-time interpretation, with string dualities manifest.