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

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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.

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Authors and Affiliations

  1. Jerusalem College of Technology, Jerusalem, 91-160, Israel

    Yaakov Friedman

  2. Department of Mathematics, University of California, Irvine, California, 92697-3875

    Bernard Russo

Authors
  1. Yaakov Friedman
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  2. Bernard Russo
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Friedman, Y., Russo, B. A New Approach to Spinors and Some Representations of the Lorentz Group on Them. Foundations of Physics 31, 1733–1766 (2001). https://doi.org/10.1023/A:1012622917155

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