A model of the two-dimensional quantum harmonic oscillator in an AdS_3 background
Abstract
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schrödinger picture in which the analogs of the Schrödinger 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 AdS_3 spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations.
- Publication:
-
European Physical Journal C
- Pub Date:
- October 2016
- DOI:
- 10.1140/epjc/s10052-016-4381-5
- arXiv:
- arXiv:1601.02838
- Bibcode:
- 2016EPJC...76..551F
- Keywords:
-
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 9 pages