Relativistic Formulation of theSU(6)Symmetry Scheme

Abstract

A relativistic formulation of the $\mathrm{SU}(6)$ symmetry scheme is presented, starting with the basic assumption that the fields corresponding to elementary particles are tensors of $M(12)$ [or $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$ or $\mathrm{SU}(12)\mathfrak{L}$]. In particular a mixed second-rank tensor and a totally symmetric third-rank tensor are associated with the meson and baryon fields, respectively. It is shown that if these fields are required to satisfy prescribed free-field equations of motion, then one is led to a particle supermultiplet structure which corresponds to the 35\ensuremath{\bigoplus}1 and 56-dimensional representations of $\mathrm{SU}(6)$ for the mesons and baryons. It is also shown that the spin-dependent and $\mathrm{SU}(3)$-spin-dependent mass splittings can be included in the theory and that solutions in terms of physical particle fields can be obtained. Effective trilinear meson-meson and meson-baryon vertex functions, using these solutions and an interaction Lagrangian which is invariant under $M(12)$, are calculated in the lowest order perturbation. We would like to note especially the following results: (a) From the known pion-nucleon coupling constant, the width of the pion-nucleon (3,3) resonance is calculated to be 94 MeV. (b) The ratio of the magnetic form factors for the neutron and proton is -⅔ for all momentum transfers and ${\ensuremath{\mu}}_{P}=(1+\frac{2{M}_{P}}{{m}_{\ensuremath{\rho}}})$ nuclear magnetons. (c) The charge form factor of the neutron is zero for all momentum transfers.