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

Frauendiener, Jörg; Sparling, George A. J.

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

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Frauendiener, Jörg
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Frauendiener, J., & Sparling, G. A. J. (1999). On a class of consistent linear higher spin equations on curved manifolds. Journal of Geometry and Physics, 30, 54-101.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-58FF-0

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.