%0 Journal Article
%T Quantum Harmonic Oscillator as a Zariski Geometry
%A Vinesh Solanki
%A Dmitry Sustretov
%A Boris Zilber
%J Mathematics
%D 2009
%I arXiv
%X We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be non-classical, in the sense that it is not interpretable in an algebraically closed field. On assuming self-adjointness of the position and momentum operators, one obtains a discrete substructure of which the original Zariski geometry is seen as the complexification.
%U http://arxiv.org/abs/0909.4415v3