Review of algebras for particle physics

The group SL(2,$\mathbb{C}$) is a suitable representation for transforming Weyl spinors and two index objects equivalent to four-vectors. In this sense, the electromagnetic four-potential also transforms under the group SL(2,$\mathbb{C}$). But, second order tensors such as the Faraday tensor  does not transform under this group. However, there is an alternative way of describing the electric and magnetic fields as a complex six-dimensional object, namely the Riemann-Silberstein vector. In this note we review different ways of transforming spinors, four-vectors and electromagnetic fields and introduce representations that combine all four Maxwell equations in a single equation.