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Irreducible Representations of Generalized Oscillator Operators
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8.see also University of Rochester Report NYO‐10241 (unpublished).
9.H. Scharfstein, Thesis (New York University, 1962).
10.The connection between spin‐1/2 angular‐momentum operators, and creation and annihilation operators satisfying anticommutation relations is well known. P. Jordan and E. P. Wigner, Z. Phys. 47, 631 (1928).
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13.O. W. Greenberg and A. Messiah (to be published). We are indebted to Prof. Greenberg for communicating these results to us prior to publication.
14.P. A. M. Dirac, Quantum Mechanics (Oxford University Press, London, 1958), pp. 144–149.
15.It has been pointed out to us by Dr. S. Okubo that this type of construction has also been used by H. J. Lipkin, “Collective Motion in Many‐Particle Systems,” Brandeis University Summer Institute Lecture Notes (W. A. Benjamin Company, Inc., New York, 1959).
16.For the particular case of operators satisfying the usual commutation relations, the fact that there is just the one familiar irreducible representation was proved by J. von Neumann, Math. Ann. 104, 570 (1931).
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