Relativistic Formulation of theSymmetry Scheme
- 6 September 1965
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 139 (5B), B1355-B1367
- https://doi.org/10.1103/physrev.139.b1355
Abstract
A relativistic formulation of the symmetry scheme is presented, starting with the basic assumption that the fields corresponding to elementary particles are tensors of [or or ]. 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 for the mesons and baryons. It is also shown that the spin-dependent and -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 , 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 nuclear magnetons. (c) The charge form factor of the neutron is zero for all momentum transfers.
Keywords
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