  We derive a modified dispersion relation (MDR) in the Lorentz violation
extension of quantum electrodynamics (QED) sector in the standard model
extension (SME) framework. Based on the extended Dirac equation and
corresponding MDR, we observe the resemblance of the Lorentz violation coupling
with spin-gravity coupling. We also develop a neutrino oscillation mechanism
induced by the presence of nondiagonal terms of Lorentz violation couplings in
2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be
Marjorana fermions. We also obtain a much stringent bound ($\backsim10^{-25}$)
on one of the Lorentz violation parameters by applying MDR to the ultrahigh
energy cosmic ray (UHECR) problem.
