Noncommutativity in field space and Lorentz invariance violation

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.