Quantum Harmonic Oscillator as a Zariski Geometry

Vinesh Solanki; Dmitry Sustretov; Boris Zilber

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arXiv · 0909.4415

Quantum Harmonic Oscillator as a Zariski Geometry

Vinesh Solanki·Dmitry Sustretov·Boris Zilber

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Abstract

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.

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BibTeX RIS

Vinesh Solanki, Dmitry Sustretov, Boris Zilber. 2013-01-25. Quantum Harmonic Oscillator as a Zariski Geometry. https://arxiv.org/abs/0909.4415

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