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Square Integrable Representations, An Invaluable Tool

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Coherent States and Their Applications

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 205))

Abstract

Square integrable representations are not only remarkable objects in abstract harmonic analysis, but also an invaluable tool in various fields of theoretical physics and applied mathematics. We will focus on the role that they play in the definition of coherent states, in wavelet analysis, in the phase-space formulation of quantum mechanics and in the associated star product formalism, and in some applications related to quantum dynamical semigroups.

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Acknowledgements

The author wishes to thank the organizers of the workshop Coherent States and Their Applications: a Contemporary Panorama (CIRM, Marseille, November 13–18, 2016).

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Authors and Affiliations

  1. Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, and Istituto Nazionale di Fisica Nucleare – Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, via Cintia, I-80126, Napoli, Italy

    Paolo Aniello

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  1. Paolo Aniello
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Correspondence to Paolo Aniello .

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Editors and Affiliations

  1. Institut de recherche en mathématique et physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  2. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Palermo, Italy

    Fabio Bagarello

  3. Laboratoire APC, Paris Diderot University, Paris, France

    Jean-Pierre Gazeau

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Aniello, P. (2018). Square Integrable Representations, An Invaluable Tool. In: Antoine, JP., Bagarello, F., Gazeau, JP. (eds) Coherent States and Their Applications. Springer Proceedings in Physics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-76732-1_2

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