The MSW Effect in Quantum Field Theory

TL;DR

This paper clarifies the connection between the Schrödinger and quantum field theory approaches to the MSW effect, detailing conditions for meaningful neutrino oscillation probabilities and their experimental relevance.

Contribution

It establishes the precise form of neutrino propagators needed in quantum field theory to define oscillation probabilities independently of production and detection processes.

Findings

Derives the relationship between Schrödinger and quantum field theory methods.

Identifies conditions where the field theory approach is applicable.

Clarifies when oscillation probabilities can be decoupled from fluxes and cross-sections.

Abstract

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.