# Projective Limits of State Spaces III. Toy-Models

Abstract : In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013) [1,2] , 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). A strategy to implement the dynamics in this formalism was presented in our first paper Lanéry and Thiemann (2017) (see also Lanéry, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization.
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https://hal.archives-ouvertes.fr/hal-01645171
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Submitted on : Thursday, November 23, 2017 - 12:52:38 AM
Last modification on : Wednesday, May 12, 2021 - 7:46:25 AM

### Citation

Suzanne Lanéry, Thomas Thiemann. Projective Limits of State Spaces III. Toy-Models. J.Geom.Phys., 2018, 123, pp.98-126. ⟨10.1016/j.geomphys.2017.08.007⟩. ⟨hal-01645171⟩

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