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Covariant Coherent States

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Coherent States, Wavelets, and Their Generalizations

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Abstract

This chapter returns to a group-theoretical context, namely, a systematic study of CS associated to group representations. After a general definition of these covariant CS, we describe the well-known Gilmore–Perelomov CS, as well as vector and matrix CS. Some generalizations are mentioned, including continuous semi-frames. We conclude the chapter by a thorough description of two interesting cases. First we treat CS on spheres constructed via heat kernels (such CS are not of the Gilmore–Perelomov type). Next we turn to CS on conformal classical domains, i.e., classical domains associated to the conformal group SO(n, 2).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada

    Syed Twareque Ali

  2. Institut de Recherche en Mathématique et Physique (IRMP), Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  3. Astroparticules et Cosmologie (APC, UMR 7164), Université Paris Diderot, Sorbonne Paris Cité Paris, France

    Jean-Pierre Gazeau

  4. Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, Brasil

    Jean-Pierre Gazeau

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Ali, S.T., Antoine, JP., Gazeau, JP. (2014). Covariant Coherent States. In: Coherent States, Wavelets, and Their Generalizations. Theoretical and Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8535-3_7

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