Abstract
A mathematical generalization of the concept of quantum spin is constructed in which the role of the symmetry groupO 3 is replaced byO v (ν=2,3,4, ...). The notion of spin direction is replaced by a point on the manifold of oriented planes in ℝv. The theory of coherent states is developed, and it is shown that the natural generalizations of Lieb's formulae connecting quantum spins and classical configuration space hold true. This leads to the Lieb inequalities [1] and with it to the limit theorems as the quantum spinl approaches infinity. The critical step in the proofs is the validity of the appropriate generalization of the Wigner-Eckart theorem.
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Lieb, E.: Commun. Math. Phys.31, 327 (1973)
Hochstadt, H.: The functions of mathematical physics. New York: Wiley 1971
Vilenkin, N.Ja.: Special functions and the theory of group representations. Providence: Am. Math. Soc. 1968
Murnaghan, F.D.: The theory of group representations. New York: Dover 1963
Schur, I.: Sitz. Preuss. Akad. Wiss. 1924, p. 297. Also Gesammelte Abhandlungen, Vol. II, p. 460. Berlin, Heidelberg, New York: Springer 1973
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Communicated by E. Lieb
This paper is based largely on the Indiana University Ph. D. thesis of the first named author
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Fuller, W., Lenard, A. Generalized quantum spins, coherent states, and Lieb inequalities. Commun.Math. Phys. 67, 69–84 (1979). https://doi.org/10.1007/BF01223201
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DOI: https://doi.org/10.1007/BF01223201