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An Obstruction to Quantizing Compact Symplectic Manifolds

Mark J. Gotay·Janusz Grabowski·Hendrik B. Grundling
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Abstract

We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.

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Mark J. Gotay, Janusz Grabowski, Hendrik B. Grundling. 1999-10-21. An Obstruction to Quantizing Compact Symplectic Manifolds. https://arxiv.org/abs/dg-ga/9706001

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