On the Groenewold-Van Hove problem for R^{2n}
Gotay, Mark J.
arXiv, 9809015 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1998-09-16
Classification:  Mathematical Physics,  Mathematics - Symplectic Geometry,  Quantum Physics 
@article{9809015,
     author = {Gotay, Mark J.},
     title = {On the Groenewold-Van Hove problem for R^{2n}},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9809015}
}

Gotay, Mark J. On the Groenewold-Van Hove problem for R^{2n}. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9809015/