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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
Article
  • 70 Downloads

Abstract

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.

Keywords

Field Theory Wave Equation Relativistic Field Lorentz Group Geometric Realization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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