The Strong Interaction Model in DFR noncommutative space-time

The Doplicher-Fredenhagen-Roberts (DFR) framework for noncommutative (NC) space-times is considered as an alternative approach to describe the physics of quantum gravity. In this formalism, the NC parameter, {\it i.e.} $\theta^{\mu\nu}$, is promoted to a coordinate of a new extended space-time. Consequently, we can construct a Field Theory in a space-time with spatial extra-dimensions. This new coordinate has a canonical momentum associated, where the effects of a new physics point of view can emerge in the fields propagation along the extra-dimension. In this paper we have introduced the gauge invariance in the DFR NC space-time by the composite symmetry $U^{\star}(N)\times U^{\star}(N)$. We have constructed the non-Abelian gauge symmetry based on DFR formalism, and we analyzed the consequences of this symmetry in the presence of such extra-dimensions. The gauge symmetry in this DFR scenario can reveal new gauge fields attached to $\theta$-extra-dimension. As an application, we have accomplished the unification of Strong Interaction with the electromagnetism and a Higgs model to give masses to the NC bosons. We have estimated their masses by using some experimental constraints of QCD.