Propagation of Electromagnetic Waves in a Degenerate Neutrino Sea

Abstract

The propagation of electromagnetic waves in a Fermi sea of neutrinos is investigated on the basis of the photon-neutrino weak-coupling theory and is compared with the result obtained by Royer on the basis of the $\left(e\nu \right)\left(e\nu \right)$ coupling. It is shown that a photon propagating through the neutrino sea satisfies a dispersion relation of the form ${\omega }^2={{\omega }_0}^2+k^2{c}^2$, where ${\left(\hslash {\omega }_0\right)}^2\approx 6.2\times {10}^{-23\mathrm{}}$ ${E_F}^2$, $E_F$ being the Fermi energy of the sea. Finally, some remarks are made as to the possibility of the destruction of a photon when propagating through the sea due to the process $\gamma +\nu \to \nu +\nu +\overline{\nu }$. It is found that the mean free path corresponding to this process is ≈ ${10}^{69}$ cm, much larger than the radius of the universe.