The quantum harmonic oscillator as a Zariski geometry

Vinesh Solanki; Dmitry Sustretov; Boris Zilber

doi:10.1016/j.apal.2014.01.002

The quantum harmonic oscillator as a Zariski geometry

Vinesh Solanki^*, Dmitry Sustretov, Boris Zilber

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field IF 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 ACF(0) and in the case F = C, is not a structure on a complex manifold. (C) 2014 Published by Elsevier B.V.

Original language	English
Pages (from-to)	1149-1168
Number of pages	20
Journal	Annals of Pure and Applied Logic
Volume	165
Issue number	6
DOIs	https://doi.org/10.1016/j.apal.2014.01.002
Publication status	Published - Jun 2014

Keywords

Interpretability
Zariski geometries

Access to Document

10.1016/j.apal.2014.01.002

http://uk.arxiv.org/abs/0909.4415

Handle.net

Persistent link

Cite this

@article{cf85ede437fa402dba4c2730aed52768,

title = "The quantum harmonic oscillator as a Zariski geometry",

abstract = "A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field IF 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 ACF(0) and in the case F = C, is not a structure on a complex manifold. (C) 2014 Published by Elsevier B.V.",

keywords = "Interpretability, Zariski geometries",

author = "Vinesh Solanki and Dmitry Sustretov and Boris Zilber",

year = "2014",

month = jun,

doi = "10.1016/j.apal.2014.01.002",

language = "English",

volume = "165",

pages = "1149--1168",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",

publisher = "Elsevier B.V.",

number = "6",

}

TY - JOUR

T1 - The quantum harmonic oscillator as a Zariski geometry

AU - Solanki, Vinesh

AU - Sustretov, Dmitry

AU - Zilber, Boris

PY - 2014/6

Y1 - 2014/6

N2 - A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field IF 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 ACF(0) and in the case F = C, is not a structure on a complex manifold. (C) 2014 Published by Elsevier B.V.

AB - A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field IF 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 ACF(0) and in the case F = C, is not a structure on a complex manifold. (C) 2014 Published by Elsevier B.V.

KW - Interpretability

KW - Zariski geometries

U2 - 10.1016/j.apal.2014.01.002

DO - 10.1016/j.apal.2014.01.002

M3 - Article (Academic Journal)

SN - 0168-0072

VL - 165

SP - 1149

EP - 1168

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 6

ER -

The quantum harmonic oscillator as a Zariski geometry

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this