Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes

In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components spin group is identified $SL(2;\mathbb{H})$, a double covering Lorentz six dimensions. We present fundamental representations show how vectors, bivectors, 3-vectors such formalism. also complexify spacetime, so that other signatures can be tackled. argue that, general, built from tensor products $SL(2;\mathbb{H})$ do not carry representation group, due to non-commutativity quaternions. The Lie algebra obtained its connection $SO(5,1)$ presented, providing physical interpretation elements $SL(2;\mathbb{H})$. Finally, bridge between spacetimes four-component over complex field comes fact Euclidean spaces given $SU(4)$.