Covariant treatment of neutrino oscillations

We derive a manifestly Lorentz-invariant formula for the oscillation probability of neutrinos using two different covariant methods. In field theory the neutrino propagation amplitude is obtained from the Feynman propagator in the time-like asymptotic limit. We find that the the phase of the transition amplitude is a factor two larger than the what is obtained in the standard derivation. We also derive the transition amplitude by the path integral method and we find the same extra factor of two in the phase. Our result implies that the upper bounds on $\Delta m^2$ obtained from neutrino oscillation experiments are a factor of two more stringent than the bounds derived from the standard oscillation formula