Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold

1997/10/22 by Mark J. Gotay, Hendrik B. Grundling
Mathematics · Physics and Astronomy · #dg-ga #math.DG #quant-ph #msc:81S99 #msc:17B66

paper · pdf

published as "Differential Geometry and Applications," I. Kolar et al., Eds., 593-596 (Masaryk University, Brno, 1999). · Plain TeX, 5 pps

arxiv created 1997/10/22 · arxiv updated 2009/11/30

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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