Relativistic Formulation of the SU(6) Symmetry Scheme
Abstract
A relativistic formulation of the SU(6) symmetry scheme is presented, starting with the basic assumption that the fields corresponding to elementary particles are tensors of M(12) [or U~(12) or SU(12)L]. In particular a mixed secondrank tensor and a totally symmetric thirdrank tensor are associated with the meson and baryon fields, respectively. It is shown that if these fields are required to satisfy prescribed freefield equations of motion, then one is led to a particle supermultiplet structure which corresponds to the 35⊕1 and 56dimensional representations of SU(6) for the mesons and baryons. It is also shown that the spindependent and SU(3)spindependent mass splittings can be included in the theory and that solutions in terms of physical particle fields can be obtained. Effective trilinear mesonmeson and mesonbaryon 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 pionnucleon coupling constant, the width of the pionnucleon (3,3) resonance is calculated to be 94 MeV. (b) The ratio of the magnetic form factors for the neutron and proton is  2/3 for all momentum transfers and μ_{P}=(1+2M_{P}m_{ρ}) nuclear magnetons. (c) The charge form factor of the neutron is zero for all momentum transfers.
 Publication:

Physical Review
 Pub Date:
 September 1965
 DOI:
 10.1103/PhysRev.139.B1355
 Bibcode:
 1965PhRv..139.1355S