By P. A. Carruthers
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Extra resources for Introduction to Unitary Symmetry
The corresponding weight diagram is displayed in Fig. 12) As shown below, the weights [eigenvalues of H, Eq. 9)] of any representation lie on a two-dimensional lattice whose translation vectors are any two of the root vectors. 13) which is demanded by the structure of the commutation rules set down below. pie is given in the following while E1P vanishes, etc. 29 SU(3): SYMMETRY IN STRONG INTERACTIONS mt Fig. 2. Weight diagram for the defining representation 3 of 5U(3). The vectors are the weight vectors, eigenvalues of the operator H.
The hCSL candidate for this is the A, since it is an isotopic singlet. Thus we have the hasic triplet . 1) where we pretend as usual that p, n, and A are degenerate. Now all particles are to he huilt up out of if; and anti-if;. This is the Sakata model (4) which was developed in the context of the group U(3) hy Ikeda, Ogawa, and Ohnuki (5). 1) are incorrect, and the Sakata model has to he abandoned in its details. We shall use the historical approach because of its intuitive appeal and because it leads naturally to the more successful "eightfold way" of GellMann (6) and Ne'eman (7).
E. Cutkosky, Ann. , 23, 415 (1963). 1 Introduction The irreducible representations of S U(3) are found by decomposing Kronecker products of 3 and 3* representations into irreducible constituents. Consider a product state composed of p functions if/' transforming like 3, and q functions