Axiomatics of particle interactions

The main point of this presentation is to explain a connection between the now celebrated work of Yang and Mills on gauge fields and some work of the authors which goes back to the same period. The work of Yang and Mills was published in 1954 and the main results were independently found by Shaw and included in his 1954 Ph.D. thesis. The authors work was done in the early 1950's, but was first published in 1963 in a long survey article on group representations. This article was based on lectures given in 1961. This work did not overlap with that of Yang, Mills, and Shaw and was done in a completely different spirit. The connection between the two is explained later in the paper. The so-called 'Yang-Mills trick' emerges naturally from a development of the authors old work on the axiomatics of quantum mechanical free particles, and in such a way as to make at least one ad hoc definition appear naturally