Infinite Multiplets and Local Fields

This paper attempts to explore, by means of a simple model without internal symmetries, the qualitative features of "local" field theories of infinite multiplets, such as are encountered in relativistic $\mathrm{SU}\left(6\right)\mathrm{}$ theory. A concept of nonderivative local interactions is defined, which leads to a generalization of conventional local field theory to include infinite representations of the spin group. Examples of these local interactions are examined in detail, and are found to have a number of attractive features. Section II of the paper is an investigation of locality in the sense of local commutation relations between the infinite-component fields. Although not conclusive, the study indicates that the conventional connection between spin and statistics gives the more physical theories, and that Fermi statistics are inconsistent with exact spin independence (invariance under the spin group).