Spontaneous Breakdown of Elementary Particle Symmetries

Following Nambu, Jona-Lasinio, and Goldstone, we seek nonperturbative solutions of quantum field theory. We first consider a model which possesses the higher symmetry $\mathrm{SU}\left(3\right)\mathrm{}$. We find that without the introduction into the Lagrangian of any symmetry-breaking terms, solutions exist which have only the lower symmetries of isotopic spin and hyperchange. We also show that the usual electrodynamic interaction of the muons and the electrons allows the possibility of generating a mass splitting between them. Finally we consider a Lagrangian in which the bare coupling constants are set equal to zero, and self-generated renormalized coupling constants are found.