Quantization and the Classical Limit

  • N. P. Landsman
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Riemannian Manifold Coherent State Poisson Bracket Heisenberg Group Classical Limit 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • N. P. Landsman
    • 1
  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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