On a class of consistent linear higher spin equations on curved manifolds

TL;DR

This paper studies a class of linear wave equations for odd half-integer spins on curved manifolds, demonstrating their well-posedness, consistency, and explicit solutions, extending the Weyl neutrino framework.

Contribution

It introduces a new class of consistent higher spin equations on curved space-times, with explicit solutions and a twistor integral representation, generalizing the Weyl neutrino equation.

Findings

Equations are well-posed in curved space-times.

Existence of invariant spinor fields indicating formal solvability.

Explicit Fourier and twistor integral solutions derived.

Abstract

We analyze a class of linear wave equations for odd half spin that have a well posed initial value problem. We demonstrate consistency of the equations in curved space-times. They generalize the Weyl neutrino equation. We show that there exists an associated invariant exact set of spinor fields indicating that the characteristic initial value problem on a null cone is formally solvable, even for the system coupled to general relativity. We derive the general analytic solution in flat space by means of Fourier transforms. Finally, we present a twistor contour integral description for the general analytic solution and assemble a representation of the group $O(4,4)$ on the solution space.