On a Microscopic Representation of Space-Time VII -- On Spin

Abstract

We recall some basic aspects of line and line Complex representations, of symplectic symmetry emerging in bilinear point transformations as well as of Lie transfer of lines to spheres. Here, we identify SU(2) spin in terms of (classical) projective geometry and obtain spinorial representations from lines, i.e.~we find a natural non-local geometrical description associated to spin. We discuss the construction of a Lagrangean in terms of line/Complex invariants. We discuss the edges of the fundamental tetrahedron which allows to associate the most real form SU(4) with its various related real forms covering SO($n$,$m$), $n+m=6$.