Meson States in a Nonlinear Spinor Model of Elementary-Particle Theory with Spontaneous Symmetry Breakdown

We consider a self-coupled spinor model of elementary particles having $S{U}_2\otimes S{U}_2$ 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.