Spin spherical harmonics from Hopf fibration: A symplectic view

We show that the embedding of the 3-sphere in C2C2 allows us to see the Hopf fibration as a symplectic flow. We also present some implications of the symplectic structure of C2C2. In particular we concentrate on some implications for the spin-weighted spherical harmonics on the sphere, and especially for the angular momentum and spin operators acting on them.