The quantum harmonic oscillator as a Zariski geometry |
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| Authors: | Vinesh Solanki Dmitry Sustretov Boris Zilber |
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| Affiliation: | 1. Heilbronn Institute for Mathematical Research, School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK;2. Department of Mathematics, Ben-Gurion University of the Negev, Yitzhak Rager Street, 84105 Be''er Sheva, Israel;3. Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford, OX1 3LB, UK |
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| 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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| Keywords: | 03C65 11R34 81R10 14A22 |
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