The spin- 1 2 singleton dipole

We establish a canonical formulation for a second-order wave equation for a spin-1/2field in a 3+2 de Sitter spacetime. We make variations of the Lagrangian, keeping the surface terms that appear in the process. By demanding that the surface terms be finite, we find that the second-order wave equation must be a singleton dipole equation. The resulting field theory exhibits a very interesting dynamics on the boundary. We study the Hamiltonian of the system and we discover that, after imposing the Lorentz condition, it reduces to an integral over a two-dimensional surface at spatial infinity.