Vector-Scalar Version of the Dirac Lagrangian

  • Patrick L. Nash


Using the recent formulation of the exceptional equivalence of a pair of real Dirac spinors and a real spacetime vector plus four real scalars, the vector-scalar equivalent of the Dirac Lagrangian is derived. The field equations associated with this new Lagrangian describe the dynamical evolution of a spin-1/2 fermion whose corresponding wave function is not a complex Dirac spinor, but is instead a real spacetime vector plus four real scalars.


Irreducible Representation Real Scalar Component Spinor Spinor Index Dirac Spinor 
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  1. 1.
    P.L. Nash, J. Math. Phys 27, 1185 (1986).CrossRefGoogle Scholar
  2. 2.
    E. Cartan, Lecons sur la theorie des spineurs (Hermann and Cie, Paris, 1938 ), Vols. I and II.Google Scholar
  3. 3.
    C. C. Chevalley, The Algebraic Theory of Spinors ( Columbia U.P., New York, 1954 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Patrick L. Nash
    • 1
  1. 1.Division of Earth and Physical SciencesThe University of Texas at San AntonioSan AntonioGermany

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