The Kummer Configuration and the Geometry of Majorana Spinors

Abstract

In this article I show how the properties of Majorana spinors in four spacetime dimensions may be understood in terms of the real projective geometry of ordinary three-dimensional space. They may be viewed as points in projective space equipped with a linear line congruence. The discrete group generated by the γ-matrices may be viewed as the automorphism group of Kummer’s configuration 16₆. As an application of line geometry which I develop I show how the skies of events of 2 + 1-dimensional Minkowski spacetime correspond to the lines of a linear line complex in projective three space.