Representations of a Gell-Mann-Dashen algebra

Astudy is made of representations of the Gell-Mann-Dashen a l g e b r a with the structure constants of an arbitrary Lie algebra on a direct integral of Hilbert spaces. In the case of the structure constants of a semisimple Lie algebra the direct integral of spaces can be reduced to an orthogonal sum of spaces, The case of the structure constants of the group 0(3) is considered in detail.