The Kummer Configuration and the Geometry of Majorana Spinors
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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.
KeywordsClifford Algebra Projective Geometry Minkowski Spacetime Line Complex Null Geodesic
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