On the Groenewold-Van Hove problem for R^{2n}
Mathematical Physics
2009-10-31 v2 math.MP
Symplectic Geometry
Quantum Physics
Abstract
We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve it when n = 1. We rigorously show that there exists an obstruction to quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap in Groenewold's original proof without introducing extra hypotheses. Moreover, when n = 1 we determine the largest Lie subalgebras of polynomials which can be unambiguously quantized, and explicitly construct all their possible quantizations.
Cite
@article{arxiv.math-ph/9809015,
title = {On the Groenewold-Van Hove problem for R^{2n}},
author = {Mark J. Gotay},
journal= {arXiv preprint arXiv:math-ph/9809015},
year = {2009}
}
Comments
15 pages, Latex. Error in the proof of Prop. 3 corrected; minor rewriting