The super-Poincaré algebra via pure spinors and the interaction principle in 3D Euclidean space

Abstract

The Poincaré superalgebra is introduced from a generalization of the Cartan's triality principle based on the extension of Chevalley product, between semispinor spaces and even subspaces of the extended exterior algebra over Euclidean space $\mathbb{R}^3$. The pure spinor formalism and the framework of Clifford algebras are used, in order to provide the necessary tools to introduce the Poincaré superalgebra where all the operators in space and superspace are constructed via pure spinors in $\mathbb{R}^3$ and the interaction principle, that generalizes the SO(8) triality principle.