The Quantum Harmonic Oscillator as a Zariski Geometry

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The Quantum Harmonic Oscillator as a Zariski Geometry

Annals of Pure and Applied Logic. 2014. Vol. 165. No. 6. P. 1149–1168.

Sustretov D., Zilber B., Solanki V.

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.

Priority areas: mathematics

Language: English

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Keywords: model theory

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Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...

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Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...

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The 17th International Summer School-Conference “Problems Allied to Model Theory and Universal Algebra” was held on 19–26 of June 2025 at Sobolev Institute of Mathematics, Novosibirsk State Technical University NETI and at the Camping Center “Erlagol” in Altai mauntains. The School was organized by Algebra and Mathematical Logic Department of Novosibirsk State Technical University (NSTU ...

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Улан-Удэ: Издательство Бурятского госуниверситета, 2017.

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