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Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold

Mark J. Gotay·Hendrik B. Grundling
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Abstract

We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Consequently there exists no finite-dimensional quantization of any Lie subalgebra of the Poisson algebra C^\infty(M) containing B.

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BibTeXRIS

Mark J. Gotay, Hendrik B. Grundling. 1997-10-22. Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold. https://arxiv.org/abs/dg-ga/9710024

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