The Kummer Configuration and the Geometry of Majorana Spinors

  • Gary W. Gibbons
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 52)


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.


Clifford Algebra Projective Geometry Minkowski Spacetime Line Complex Null Geodesic 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Gary W. Gibbons
    • 1
  1. 1.DAMTPUniversity of CambridgeCambridgeUK

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