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Quantum Frames, Quantization and Dequantization

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Quantization and Infinite-Dimensional Systems

Abstract

A continuous frame in a Hilbert space is a concept well adapted for constructing very general classes of coherent states, in particular those associated to group representations which are square integrable only on a homogeneous space. In addition, (quantum) frames provide a method of quantization which generalizes the coherent state approach and fits in neatly with the operational meaning of quantum measurements. We discuss this approach in detail, taking as our working example the case of the Poincaré group in 1+1 space-time dimensions. We also compare this approach to the familiar geometric quantization method, which turns out to be less versatile than the new one.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, Montreal, Canada, H4B 1R6

    S. Twareque Ali & J.-P. Antoine

  2. Institut de Physique Théorique, Université Catholique de Louvain, B - 1348, Louvain-la-Neuve, Belgium

    J.-P. Antoine

Authors
  1. S. Twareque Ali
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  2. J.-P. Antoine
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Editor information

Editors and Affiliations

  1. Catholic University of Louvain, Louvain-la-Neuve, Belgium

    J-P. Antoine

  2. Concordia University, Montréal, Québec, Canada

    S. Twareque Ali

  3. Warsaw University, Białystok, Poland

    W. Lisiecki  & A. Odzijewicz  & 

  4. Bulgarian Academy of Sciences, Sofia, Bulgaria

    I. M. Mladenov

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© 1994 Springer Science+Business Media New York

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Ali, S.T., Antoine, JP. (1994). Quantum Frames, Quantization and Dequantization. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization and Infinite-Dimensional Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2564-6_16

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  • DOI: https://doi.org/10.1007/978-1-4615-2564-6_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6095-7

  • Online ISBN: 978-1-4615-2564-6

  • eBook Packages: Springer Book Archive

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