Noncommutativity in Field Space and Lorentz Invariance Violation

TL;DR

This paper explores how noncommutativity in field space can lead to Lorentz invariance violation, deriving a new dispersion relation and discussing implications for cosmic ray physics and matter-antimatter asymmetry.

Contribution

It introduces a novel dispersion relation in a noncommutative field theory with a single new parameter, linking noncommutativity to potential observable effects.

Findings

Noncommutative scale constrained by current experiments.

Cosmic ray physics remains compatible with quantum gravity-induced noncommutativity.

Matter-antimatter asymmetry arises naturally in this framework.

Abstract

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.