A relativistic formulation of the $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry scheme is presented, starting with the basic assumption that the fields corresponding to elementary particles are tensors of $M\left(12\right)\mathrm{}$ [or $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$ or $\mathrm{SU}\left(12\right)\mathrm{}\mathfrak{L}$]. 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⊕1 and 56-dimensional representations of $\mathrm{SU}\left(6\right)\mathrm{}$ for the mesons and baryons. It is also shown that the spin-dependent and $\mathrm{SU}\left(3\right)\mathrm{}$-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 $M\left(12\right)\mathrm{}$, 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 ${\mu }_P=(1+\frac{2M_P}{m_{\rho }})$ nuclear magnetons. (c) The charge form factor of the neutron is zero for all momentum transfers.

• Received 22 March 1965

DOI:https://doi.org/10.1103/PhysRev.139.B1355