Conjugate spinor field equation for massless spin-$\frac{3}{2}$ field in de Sitter ambient space

Abstract

The quantum field theory in de Sitter ambient space provide us with a comprehensive
description of massless gravitational field.
Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.
In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.