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Coherent states and induced representations

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Abstract

A generalization of the notion of coherent states is given. The following one-to-one correspondences are pointed out: (1) between covariant overcomplete systems of coherent states and a class of covariant semi-spectral measures; (2) between covariant semispectral measures and unitary irreducible subrepresentations of induced representations of Lie groups; (3) between unitary irreducible representations of Lie groups with covariant overcomplete systems of coherent states and unitary irreducible subrepresentations of induced representations, whose representation spaces are reproducing kernel Hilbert spaces.

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  1. Dept. of Fundamental Physics, Institute of Physics and Nuclear Engineering, P.O. Box 5206, Bucharest, Romania

    H. Scutaru

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  1. H. Scutaru
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Scutaru, H. Coherent states and induced representations. Lett Math Phys 2, 101–107 (1977). https://doi.org/10.1007/BF00398574

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  • DOI: https://doi.org/10.1007/BF00398574

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