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The quantum harmonic oscillator as a Zariski geometry

Authors
  • Solanki, Vinesh
  • Sustretov, Dmitry
  • Zilber, Boris1, 2, 3, 4, 5, 6, 7, 8
  • 1 Heilbronn Institute for Mathematical Research
  • 2 School of Mathematics
  • 3 University of Bristol
  • 4 University Walk
  • 5 Department of Mathematics
  • 6 Ben-Gurion University of the Negev
  • 7 Mathematical Institute
  • 8 University of Oxford
Type
Published Article
Journal
Annals of Pure and Applied Logic
Publication Date
Jan 01, 2014
Accepted Date
Dec 12, 2013
Identifiers
DOI: 10.1016/j.apal.2014.01.002
Source
Elsevier
Keywords
License
Unknown

Abstract

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field F 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 ACF0 and in the case F=C, is not a structure on a complex manifold.

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