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Finite and Disconnected Subgroups of SU 3 and their Application to the Elementary‐Particle Spectrum
1.R. E. Behrends, J. Dreitlein, C. Fronsdal, and B. W. Lee, Rev. Mod. Phys. 34, 1 (1962).
2.M. Gell‐Mann, “The Eightfold Way,” CTSL‐20 (1961);
2.Phys. Rev. 125, 1067 (1962).
3.Y. Ne’eman, Nucl. Phys. 26, 222 (1961).
4.See for example, T. D. Lee and C. N. Yang, Phys. Rev. 122, 1954 (1961).
5.D. R. Speiser and J. Tarski, J. Math. Phys. 4, 588 (1963) (preprint version).
6.G. A. Miller, H. F. Dickson, and L. E. Blichfeldt, Theory and Applications of Finite Groups (G. E. Stechert and Company, New York, 1938), Chap. XII.
7.C. Jordan, J. Reine Angew. Math. 84, 93 (1878).
8.C. Jordan, Atti Reale Accad. Napoli, 8, No. 11 (1879).
9.M. Hamermesh, Group Theory (Addison Wesley Publishing Company, Reading, Massachusetts, 1962), Chap. 9, Sec. 7.
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14.J. J. Sakurai, Phys. Rev. Letters 10, 446 (1963).
15.D. E. Littlewood, The Theory of Group Characters (The Clarendon Press, Oxford, England, 1940), Chap. 9.
16.Reference 15, Appendix.
17.See for example, J. S. Lomont, Applications of Finite Groups (Academic Press Inc., New York, 1959), Chap. 5.
18.For details of the explicit construction of these representations, see W. H. Klink, “Finite and Disconnected Subgroups of and their Application to the Elementary Particle Spectrum,” dissertation, Johns Hopkins University, Baltimore, Maryland, 1963 (unpublished).
19.Reference 9, p. 104.
20.To subduce means to take away those elements of a group G not in its subgroup H. See Ref. 17, p. 219.
21.If an element corresponding to a rotation of about an axis (p,n integer, ) is related to some observable quantity (say charge), then it is conserved modulo n. In the limit this quantity will be conserved exactly.
22.P. Tarjanne, Physica 105, (1962).
23.It may appear puzzling that generators for all the Σ groups given in Table I are 3‐dimensional and therefore seem to provide a counterexample to the result we have just obtained. These matrices generate 3‐dimensional representations of subgroups of In those cases, where the subgroups of differ from those of we must factor out the center to obtain the groups corresponding to The 3‐dimensional representations would then disappear. These considerations do not affect our character tables.
24.There is also no longer any reason why σ groups other than should not be analyzed. For convenience we will continue the analysis with The results we obtain will be typical of the other Σ groups.
25.S. Gasiorowicz, “A Simple Graphical Method in the Analysis of ” ANL‐6729 (1963).
26.S. Weinberg, “On the Derivation of Intrinsic Symmetries” (1963) (preprint).
27.Reference 17, p. 23.
28.H. Weyl, The Classical Groups (Princeton University Press, Princeton, New Jersey, 1939), Chap. 6, See. 5.
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