Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold
dg-ga
2007-05-23 v1 Differential Geometry
Quantum Physics
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.
Keywords
Cite
@article{arxiv.dg-ga/9710024,
title = {Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold},
author = {Mark J. Gotay and Hendrik B. Grundling},
journal= {arXiv preprint arXiv:dg-ga/9710024},
year = {2007}
}
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