Yang-Mills-Shaw and the non-Abelian Maxwell equations

This paper sets out to present, in a brief and intuitive way, fundamental aspects on the construction and formulation of the Yang-Mills-Shaw Theory. Starting off from the paradigm of Maxwell Electromagnetism, we build up, by analogy, the formulation for nonabelian vector fields and their (gauge) interactions with matter. In order to do so, we extend $\text{U}(1)$ to the $\text{SU}(N)$ group and write down the nonabelian extension of the Maxwell equations by now defining the electric and magnetic fields for the $\text{SU}(N)$-symmetry.

Keywords:
Group theory; invariance and symmetry; particle physics