Photons, neutrinos, and the optical activity

We compute the one-loop helicity amplitudes for low-energy nu gamma-->nu gamma scattering and its crossed channels in the standard model with massless neutrinos. In the center of mass, with roots = 2 omega << 2m(e), the cross sections for these 2-->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 nonzero. 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 in the absence of dispersion.