Coherent states and induced representations |
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Authors: | H. Scutaru |
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Affiliation: | (1) Dept. of Fundamental Physics, Institute of Physics and Nuclear Engineering, P.O. Box 5206, Bucharest, Romania |
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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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