Projective Limits of State Spaces II. Quantum Formalism

Understand

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a quantum theory as projective families of density matrices.

• After discussing the formalism at the classical level in a first paper, 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.
• Regarding the quantization of classical projective structures into quantum ones, we extend the results by Oko{\l}\'ow [Oko{\l}\'ow 2013, arXiv:1304.6330], 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.