The MSW Effect in Quantum Field Theory

We show in detail the general relationship between the Schr\"{o}dinger equation approach to calculating the MSW effect and the quantum field theoretical S-matrix approach. We show the precise form a generic neutrino propagator must have to allow a physically meaningful ``oscillation probability'' to be decoupled from neutrino production fluxes and detection cross-sections, and explicitly list the conditions---not realized in cases of current experimental interest---in which the field theory approach would be useful.