Foundations of Physics

, Volume 31, Issue 12, pp 1733–1766 | Cite as

A New Approach to Spinors and Some Representations of the Lorentz Group on Them

  • Yaakov Friedman
  • Bernard Russo


We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin-\({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\) wave equations of relativistic field theory, showing some unexpected relations between various low-dimensional Lorentz representations. We include a geometrically and physically motivated introduction to Jordan triples and spin factors.


Field Theory Wave Equation Relativistic Field Lorentz Group Geometric Realization 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Yaakov Friedman
    • 1
  • Bernard Russo
    • 2
  1. 1.Jerusalem College of TechnologyJerusalemIsrael
  2. 2.Department of MathematicsUniversity of CaliforniaIrvine

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