On theSU(3) Unitary Representations

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Abstract
The unitary representations of the SU(3) group are investigated in the Fock space defined by the Bose creation annihilation operators ak, ai, b†iandb†k (i, k = 1, 2, 3). We obtain the projection operators that pick up the vectors in the space of the arbitrary unitary representations of the SU(3) group out of the Fock space. By the use of those projection operators, the canonical basis vectors |TµY(p, q)> are explicitly obtained without the SU(3) C.-G. coefficients. Each normalized isoscalar factor of the SU(3) C.-G. coefficient in the coupling of D(p, 0) and D(0, q) is given in terms of the arbitrary irreducible representation. It is seen that all the possible SU(3) transitions between the vectors of the arbitrary irreducible representation spaces occur by applying the irreducible tensor operators in the Fock space. The extension of the Bose operator method to the SU(N) group is performed by introducing Bose creation annihilation operators with totally antisymmetric indices.

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