4-Spinors and a Projection onto 3+1 Spacetime

Abstract

We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural expression in terms of these primitive spinor variables, while an ordinary spacetime interpretation may be obtained by projecting solutions. Using this projection, we show how the real components of a given 4-spinor reference a point in a five dimensional spacetime.