Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold
Mark J. Gotay, Hendrik B. Grundling
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∞(M) containing B.
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