The quantum harmonic oscillator as a Zariski geometry

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Annals of Pure and Applied Logic 165 (6):1149-1168 (2014)
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Abstract

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field FF of characteristic 0, which is shown to be uncountably categorical. An analysis of definable sets is carried out, from which it follows that this structure is a Zariski geometry of dimension 1. It is non-classical in the sense that it is not interpretable in ACF0ACF0 and in the case F=CF=C, is not a structure on a complex manifold

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10.1016/j.apal.2014.01.002

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Generalised imaginaries and galois cohomology.Dmitry Sustretov - 2016 - Journal of Symbolic Logic 81 (3):917-935.

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