  We use previous work on the Hilbert space for mixed fields to derive deformed
dispersion relations for neutrino flavor states. We then discuss how these
dispersion relations may be incorporated into frameworks encoding the breakdown
of Lorentz invariance. We consider non-linear relativity schemes (of which
doubly special relativity is an example), and also frameworks allowing for the
existence of a preferred frame. In both cases we derive expressions for the
spectrum and end-point of beta decay, which may be used as an experimental
probe of the peculiar way in which neutrinos experience Lorentz invariance.
