Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33369We 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.Plain TeX, 5 ppsDifferential GeometryQuantum Physics81S99 (Primary) 17B66 (Secondary)Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifoldtext