On ultra-relativistic approximations, unobservable phases and other hand-waving in the derivation of the neutrino oscillation length

Abstract

A wrong derivation of the phase of a propagating massive particle which has repeatedly appeared during the last years has the advantage of leading once more to the important question of the phase difference between the mass eigenstates constitutive of an oscillating neutrino described in the plane wave formalism. Serious errors of principle are pointed at in a number of simple calculations and the oscillation length is derived in a way which allows to show that the standard result can suffer but minute variations in the ultrarelativistic case.