# Projective Limits of State Spaces II. Quantum Formalism

Abstract : In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). 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] .
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https://hal.archives-ouvertes.fr/hal-01553847
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Submitted on : Monday, July 3, 2017 - 5:28:34 PM
Last modification on : Tuesday, May 11, 2021 - 11:16:44 PM

### Citation

Suzanne Lanéry, Thomas Thiemann. Projective Limits of State Spaces II. Quantum Formalism. J.Geom.Phys., 2017, 116, pp.10-51. ⟨10.1016/j.geomphys.2017.01.011⟩. ⟨hal-01553847⟩

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