The Yang-Mills gauge theory in DFR noncommutative space-time

TL;DR

This paper develops a gauge-invariant non-Abelian gauge theory within the DFR noncommutative space-time framework, incorporating extra dimensions associated with the noncommutative parameter and exploring the resulting gauge field dynamics.

Contribution

It introduces gauge invariance in the DFR noncommutative space-time and analyzes the implications of non-Abelian gauge symmetry with extra-dimensional effects.

Findings

Formulation of gauge invariance in DFR noncommutative space-time

Derivation of gauge field propagation in extra dimensions

Identification of new fields linked to the noncommutative parameter

Abstract

The Doplicher-Fredenhagen-Roberts (DFR) framework for noncommutative (NC) space-times is considered as an alternative approach to describe the physics of quantum gravity, for instance. 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 have 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 can emerge in the fields propagation along the extra-dimension. In this paper we introduce the gauge invariance in the DFR NC space-time. We present the non-Abelian gauge symmetry in DFR formalism, and the consequences of this symmetry in the presence of such extra-dimension. The gauge symmetry in this DFR scenario can reveal new fields attached to $\theta$-extra-dimension. We obtain the propagation of these gauge fields in terms of canonical momentum associated with $\theta$-coordinate.