Celebrating the 70th anniversary of the publication of the paper by C. N. Yang and R. Mills, this paper proposes to present the construction of the so-called Yang-Mills equations based on fundamental requirements, investigating how one can formulate a theory that describes the self-interaction of electromagnetically neutral vector bosons with zero mass. As these are attributes of the photon, the starting point is Maxwell’s equations and their so-called local gauge invariance, with symmetry group U(1). Thus, starting from a set of vector fields that have an associated global non-Abelian symmetry, we will use the so-called Noether current method to introduce self-interactions. The interesting aspect is that this process concludes with the starting symmetry, initially global, automatically becoming a gauge symmetry as a result of the structure of the self-interactions. The approach already leaves the path built for the introduction of the matter sector minimally coupled to the Yang-Mills fields. It is important to highlight that this procedure goes in the opposite direction to what is presented in the original paper by Yang-Mills. The procedure via Noether currents is more natural, as it answers the question how elementary spin-1 particles can self-interact, without needing to appeal to matter fields.
Keywords
Self-interacting spin-1 bosons; non-Abelian gauge theory; Noether current method