Abstract
The aim of quantization theory as presented in this book is to relate Poisson algebras or Poisson manifolds to C*-algebras or their pure state spaces. A slightly awkward feature of the first relationship is that usually Poisson algebras are not Banach spaces; a nonzero Poisson bracket on some Poisson subalgebra \(\widetilde{\mathfrak{A}}_{\mathbb{R}}^{0}ofC_{b}^{\infty }(P,\mathbb{R}{\text{)}}\) cannot be extended to the closure \(\mathfrak{A}_{\mathbb{R}}^{0}of\widetilde{\mathfrak{A}}_{\mathbb{R}}^{0}\) in the sup-norm.
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© 1998 Springer Science+Business Media New York
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Landsman, N.P. (1998). Quantization and the Classical Limit. In: Mathematical Topics Between Classical and Quantum Mechanics. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1680-3_3
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DOI: https://doi.org/10.1007/978-1-4612-1680-3_3
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