  The connection between Lorentz invariance violation and noncommutativity of
fields in a quantum field theory is investigated. A new dispersion relation for
a free field theory with just one additional noncommutative parameter is
obtained. While values for the noncommutative scale much larger than 10^{-20}
eV^{-1} are ruled out by the present experimental status, cosmic ray physics
would be compatible with and sensible to a noncommutativity arising from
quantum gravity effects. We explore the matter-antimatter asymmetry which is
naturally present in this framework.
