Projective limits of state spaces II. Quantum formalism

After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1)  [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].