General Relativity and Gravitation

, Volume 5, Issue 6, pp 621–642

The neutrino energy-momentum tensor and the Weyl equations in curved space-time

  • Ian M. Anderson
Research Articles

DOI: 10.1007/BF00761921

Cite this article as:
Anderson, I.M. Gen Relat Gravit (1974) 5: 621. doi:10.1007/BF00761921


In general, a first order Lagrangian gives rise to second order Euler-Lagrange equations. However, there are important examples where the associated Euler-Lagrange equations are of first order only, the Weyl neutrino equations being of this type. In this paper we therefore consider first order spinor Lagrangians which give rise to firstorder Euler-Lagrange equations. Specifically, the most general first order spinor field equations of rank one in curved space-time which are derivable from a first order Lagrangian of the same type are explicitly constructed. Subject to a certain restriction, the Weyl neutrino equation is the only possibility. Furthermore, if the spinor field satisfies the Weyl neutrino equation, then the associated energy momentum tensor is the conventional neutrino energymomentum tensor.

Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Ian M. Anderson
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of MathematicsUniversity of ArizonaTucson

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