Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold

Details Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold

1997-10-22

arxiv.org/abs/dg-ga/9710024v1

"Differential Geometry and Applications," I. Kolar et al., Eds., 593-596 (Masaryk University, Brno, 1999).

Mathematics

Differential Geometry

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Scientific paper

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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