Some aspects of field symmetries. III

Some aspects of the connection between trilinear and bilinear equal-time commutation relations are clarified. Locality requirements satisfied by the generalized fields under discussion are examined in some detail. Using algebraic arguments it is shown that for representations of operators satisfying the generalized trilinear equal-time commutation relations either the half-integral- or the integral-spin fields or both satisfy conventional statistics. In connection with a question raised previously it is shown that the hadronic schemes considered suggest which fields should in each scheme be associated with the (hypothetical) intermediate bosons. It is shown that the discrepancy in physical content between the various particle classification schemes discussed can be substantially reduced, if not eliminated, by the introduction of a new selection rule in addition to the selection rules derived from locality and self-adjointness of the Lagrangian. The new selection rule is not unrelated to locality considerations and is also related to the metric. The question of the metric in the context of the generalized fields is briefly considered.