On the Groenewold-Van Hove problem for R^{2n}

Details On the Groenewold-Van Hove problem for R^{2n} On the Groenewold-Van Hove problem for R^{2n}

1998-09-16

arxiv.org/abs/math-ph/9809015v2

J.Math.Phys. 40 (1999) 2107-2116

Physics

Mathematical Physics

15 pages, Latex. Error in the proof of Prop. 3 corrected; minor rewriting

Scientific paper

10.1063/1.532854

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.

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