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Differential Geometry, Group Representations, and Quantization pp 145–178Cite as

Quantization, coherent states and diffeomorphism groups

  • Part III: General Qauntization Methods
  • Conference paper
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Part of the book series: Lecture Notes in Physics ((LNP,volume 379))

Abstract

We suggest extending the method of coherent-states quantization, which applies to homogeneous spaces for locally compact groups, to the case of infinite-dimensional groups such as diffeomorphism groups. Such a framework could unify a number of different approaches to quantum theory. We review some relevant results and examples, and take a first step in this program by demonstrating that the unitary representation of Diff(IR) obtained from the “single-particle” coadjoint orbit is in fact square-integrable.

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Authors and Affiliations

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

    S. Twareque Ali

  2. Departments of Mathematics and Physics, Rutgers University, New Brunswick, 08903, New Jersey, U S A

    Gerald A. Goldin

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  1. S. Twareque Ali
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  2. Gerald A. Goldin
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Jö-Dieter Hennig Wolfgang Lücke Jiří Tolar

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© 1991 Springer-Verlag

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Twareque Ali, S., Goldin, G.A. (1991). Quantization, coherent states and diffeomorphism groups. In: Hennig, JD., Lücke, W., Tolar, J. (eds) Differential Geometry, Group Representations, and Quantization. Lecture Notes in Physics, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53941-7_10

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  • DOI: https://doi.org/10.1007/3-540-53941-7_10

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  • Online ISBN: 978-3-540-46473-0

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