A model of the two-dimensional quantum harmonic oscillator in an $AdS_3$ background
General Relativity and Quantum Cosmology
2016-10-28 v2 High Energy Physics - Theory
Quantum Physics
Abstract
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the spacetime. In this picture, we have a metamorphosis of the Heisenberg's uncertainty relations.
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Cite
@article{arxiv.1601.02838,
title = {A model of the two-dimensional quantum harmonic oscillator in an $AdS_3$ background},
author = {Rudolf Frick},
journal= {arXiv preprint arXiv:1601.02838},
year = {2016}
}
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9 pages