Neutrino oscillations are examined under the broad requirements of Poincaré-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The aim of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable and how many factors that are important in principle end up being negligible in practice.
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