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We consider a self-coupled spinor model of elementary particles having SU₂U₂ symmetry. We demonstrate that for the case of complete spontaneous breakdown of the isospin symmetry the bubble approximation gives a method for treating the meson states that is compatible with symmetries of the model in that it gives the Goldstone bosons and Goldberger-Treiman relations exactly. We also show that by a continuation in the parameter characterizing the isospin breakdown we can transform from a solution having isospin degeneracy to solutions in which the isospin, as well as the chiral symmetry is spontaneously broken. Calculational techniques for our approximation are explicitly given.
Byrne et al. (Mon,) studied this question.
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