Some Considerations on Nonlinear Realizations of ChiralSU(3)×SU(3)

Abstract

We consider how nonlinear realizations of the chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry arise in certain limits of models in which fields transform linearly under the group of transformations which leave the Lagrangian (approximately) invariant. All possible cases of nonlinear realizations of the chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$, wherein at least the $U\left(2\right)\mathrm{}$ group generated by isospin and hypercharge is linearly represented, are considered. The connection between the nonlinear realizations and the spontaneous breakdown of the symmetry is made clear. Our results are clarified from a group-theoretic point of view, thereby establishing the connection between our results and a more general consideration of Coleman et al. We discuss theoretical and experimental implications of nonlinar realizations of the chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$, with reference to the $\kappa$ meson.