Coherent Neutrino Propagation in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we have studied the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum $p\sim G_F\rho/\sqrt{2}$. We have studied in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic ``Standard Model'' with two neutrino flavours. For a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos