Volume 20, Issue 3, October 2013, Pages 420 - 430
Coadjoint Orbits of Certain Motion Groups and Their Coherent States
Authors
Majdi Ben Halima
Faculty of Sciences at Sfax, Department of Mathematics, University of Sfax Route de Soukra, B.P. 1171 3000-Sfax, Tunisia,majdi.benhalima@yahoo.fr
Received 22 May 2013, Accepted 19 July 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.855046How to use a DOI?
- Keywords
- Motion group; coadjoint orbit; coherent state; dequantization
- Abstract
Let ℍn, n ≥ 1, be the (2n+1)-dimensional Heisenberg group and let K be a closed connected subgroup of the unitary group U(n) acting on ℍn by automorphisms. Using the moment map, we provide in this paper a dequantization procedure for all generic admissible coadjoint orbits of the semidirect product G = K ⋉ ℍn. In the opposite direction, we show that Gilmore-Perelomov's coherent states define “pure state quantizations” of such orbits.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Majdi Ben Halima PY - 2021 DA - 2021/01/06 TI - Coadjoint Orbits of Certain Motion Groups and Their Coherent States JO - Journal of Nonlinear Mathematical Physics SP - 420 EP - 430 VL - 20 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.855046 DO - 10.1080/14029251.2013.855046 ID - Halima2021 ER -