The Kummer Configuration and the Geometry of Majorana Spinors
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
Unable to display preview. Download preview PDF.
- L. Dabrowski, Group Actions on Spinors Bibliopolis (1988)Google Scholar
- A. S. Eddington, New Pathways in Science Cambridge University Press p.271 (1935)Google Scholar
- A. S. Eddington, Relativity Theory of Electrons and Protons Cambridge University Press p.36 (1936)Google Scholar
- A. S. Eddington, The New Statesman and Nation Dec 19 1936 p 1044, Jan 9 1937 pp. 62–64.Google Scholar
- E.R. Paërls, Representations of the Lorentz Group and Projective Geometry Google Scholar