The Neutrino Energy-Momentum Tensor and the Weyl Equations in Curved Space-Time

Document Type

Article

Journal/Book Title/Conference

General Relativity and Gravitation

Volume

5

Issue

6

Publication Date

1974

First Page

621

Last Page

642

Abstract

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.

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Published by Springer in General Relativity and Gravitation. Publisher PDF is available through link above. Publisher requires a subscription to access article.

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