  Loop quantum gravity theory incorporates a new scale length ${\cal L}$ which
induces a Lorentz invariance breakdown. This scale can be either an universal
constant or can be fixed by the momentum of particles (${\cal L}\sim p^{-1}$).
Effects of the scale parameter ${\cal L}$ and helicity terms occurring in the
dispersion relation of fermions are reviewed in the framework of spin-flip
conversion of neutrino flavors.
