Photons, neutrinos and optical activity

We compute the one-loop helicity amplitudes for low-energy $\nu \gamma \to \nu \gamma$ scattering and its crossed channels in the standard model with massless neutrinos. In the center of mass, with $\sqrt{s} = 2\omega\ll 2m_e$,thecrosssectionsforthese$2\to 2$ channels grow roughly as ${\omega }^6$. The scattered photons in the elastic channel are circularly polarized and the net value of the polarization is non-zero. We also present a discussion of the optical activity of a sea of neutrinos and estimate the values of its index of refraction and rotary power.