Abstract
It is shown that the possibility of representing every operator, acting on a vector space, irreducible under SU(2), in the form f|Ω>G(Ω)<Ω| dΩ [1], where {|Ω>} is a set of Bloch (atomic) coherent states, can be generalized to compact semi-simple Lie groups.
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References
ArecchiF.T., et al., Phys. Rev. A6, 2211 (1972).
PerelomovA.M., Commun. Math. Phys. 26, 222 (1972).
OnofriE., J. Math. Phys. 16, 1087 (1975).
Warner, G., Harmonic Analysis on Semi-Simple Lie Groups I, Springer Verlag, 1972, Chapter I.
Serré, J.-P., Représentations linéaires et espaces homogènes Kaehleriens des groupes de Lie semi-simples compacts, Sém. Bourbaki, Exp. 100 (1954).
KobayashiS. and NomizuK., Foundations of Differential Geometry, Interscience, New York, 1963.
Bochner, S. and Martin, W., Several Complex Variables, Princeton University Press, 1948, p. 139.
VladimirovV.S., Les fonctions de plusieurs variables complexes, Dunod, Paris, 1967, p. 39.
DixmierJ., Les C *-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964, p. 261.
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Supported by the Swiss National Science Foundation.
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Romerio, M. On the coherent state representation of linear operators. Lett Math Phys 2, 27–31 (1977). https://doi.org/10.1007/BF00420667
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DOI: https://doi.org/10.1007/BF00420667