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            <title xml:lang="en">Projective Limits of State Spaces III. Toy-Models</title>
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                <forename type="first">Suzanne</forename>
                <surname>Lanéry</surname>
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            <idno type="halRefHtml">&lt;i&gt;J.Geom.Phys.&lt;/i&gt;, 2018, 123, pp.98-126. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.geomphys.2017.08.007"&gt;&amp;#x27E8;10.1016/j.geomphys.2017.08.007&amp;#x27E9;&lt;/a&gt;</idno>
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            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
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                    <forename type="first">Suzanne</forename>
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                <term xml:lang="en">Projective limits</term>
                <term xml:lang="en">Fock space</term>
                <term xml:lang="en">density matrix</term>
                <term xml:lang="en">nonrelativistic</term>
                <term xml:lang="en">Schroedinger equation</term>
                <term xml:lang="en">toy model</term>
                <term xml:lang="en">quantization</term>
                <term xml:lang="en">model: linear</term>
                <term xml:lang="en">field theory: classical</term>
                <term xml:lang="en">Algebras of observables</term>
                <term xml:lang="en">Regularization</term>
                <term xml:lang="en">Fock representation</term>
                <term xml:lang="en">Second quantization</term>
                <term xml:lang="en">Quantum field theory</term>
                <term xml:lang="en">81T27</term>
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              <p>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.</p>
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