Variational Field Equations of a Majorana Neutrino Coupled to Einstein's Theory of General Relativity

TL;DR

This paper derives the coupled equations for a Majorana neutrino in general relativity using a variational approach, demonstrating the equivalence of different formulations and clarifying the role of Belinfante-Rosenfeld forms.

Contribution

It provides a consistent variational derivation of Majorana neutrino field equations coupled to gravity, highlighting the use of Belinfante-Rosenfeld forms for energy-momentum tensor symmetrization.

Findings

Explicit demonstration of equivalence between first and second order field equations

Identification of Lagrange multiplier 2-forms as Belinfante-Rosenfeld forms

Clarification of energy-momentum tensor symmetrization in spinor-gravity coupling

Abstract

A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The Lagrange multiplier 2-forms we use turn out to be precisely the Belinfante-Rosenfeld 2-forms that are needed to symmetrize the canonical energy-momentum tensor of the Majorana spinor.