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

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.

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

References in corpus (4)

• Obstructions to Quantization
• Obstruction Results in Quantization Theory
• On Quantizing $T^{\ast }{S}^1$
• Geometric Quantization and No Go Theorems

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