Gauge-invariant matter field actions from an iterative Noether coupling

Generalizing Deser’s work on pure $SU(2)$ gauge theory, we consider scalar, spinor, and vector matter fields transforming under arbitrary representations of a non-Abelian, compact, semisimple internal Lie group, which is a global symmetry of their actions. These matter fields are coupled to Abelian gauge fields through the process of iterative Noether coupling. This procedure is shown to yield precisely the same locally gauge invariant theory (with the non-Abelian group as the gauge group) as obtained by the usual minimal coupling prescription originating from the gauge principle. Prospects of this nongeometrical formulation, towards a better understanding of physical aspects of gauge theories, are briefly discussed.