Neutrino mixing and Lorentz invariance

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. (authors)