Optical activity of a neutrino sea in the Standard Model

We present the Standard Model calculation of the optical activity of a neutrino sea. The idea that intergalactic space is a birefrigent medium for light due to the presence of a neutrino sea has been contemplated for a long time. Some thirty years ago, Royer [1] computed in V − A theory an effect of order G F . Later, Stodolsky noted that due to a theorem of Gell-Mann [2], there can be no such effect with massless neutrinos and a point-like coupling, and his observation was recorded by one of the present authors in a review [3]. In the early 1980’s data on propagation of radio waves through intergalactic Space put a stringent upper bound on possible optical activity of the neutrino sea [4] and [5] and this led to renewed estimates for the size of such effect on the assumption of a neutrino magnetic moment, which occur for a massive neutrino [5]. More recently [6] an evaluation was made for a off-mass shell photons within the Standard Model (SM). Here we note that there is a frequency dependent effect even for real photons and we also comment on the effect for virtual photons (both within the SM). Thus we shall consider three possible effects: a magnetic moment effect, an effect for virtual photons, an effect for real photons.