Rendering SU(3) intuitive: Symmetries of Lorentz tensors

Abstract : Under a Lorentz transformation of the electromagnetic field (E, cB) the quantity E$^2$ − c$^2$B$^2$ remains preserved. A Lorentz transformation does not preserve the energy density ε$_0$ (E$^2$ + c$^2$B$^2$) of the field. One can thus ask which are the transformations that preserve the quantity E$^2$ + c$^2$B$^2$. We show that the symmetry group of such transformations is isomorphic to SU(3). We can thus use these transformations of the electromagnetic field as a model to visualize what happens in SU(3) by analogy, just like we can use the rotation group SU(2) as a model to visualize what happens in the isospin group SU(2) by analogy.