On the $\star$-product quantization and the Duflo map in three dimensions
High Energy Physics - Theory
2012-11-01 v2 Mathematical Physics
math.MP
Abstract
We analyze the star product induced on the algebra of functions on R^3 by a suitable reduction of the Moyal product defined on F(R^4). This is obtained through the identification of R^3 with the dual of a three dimensional Lie algebra. We consider the su(2) case, exhibit a matrix basis and realize the algebra of functions on its dual in such a basis. The relation to the Duflo map is discussed. As an application to quantum mechanics we compute the spectrum of the hydrogen atom.
Keywords
Cite
@article{arxiv.1209.2941,
title = {On the $\star$-product quantization and the Duflo map in three dimensions},
author = {Luigi Rosa and Patrizia Vitale},
journal= {arXiv preprint arXiv:1209.2941},
year = {2012}
}
Comments
Misprints corrected. Journal ref. added