Yang-Mills theory for nonsemisimple groups

For semisimple groups, possibly multiplied by U(1)’s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for nonsemisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such nonsemisimple Yang-Mills theories may lead to physical consequences worth studying. The nonsemisimple group with only two generators that do not commute is studied in detail.