The standard electroweak model in the noncommutative $DFR$ space-time

TL;DR

This paper constructs a Lorentz-invariant noncommutative version of the Standard Model using the DFR framework, incorporating spontaneous symmetry breaking and calculating new boson masses.

Contribution

It develops a noncommutative electroweak model within the DFR formalism, including symmetry breaking and mass spectrum analysis, extending prior noncommutative approaches.

Findings

Electroweak symmetry breaking analyzed in DFR framework

Masses of new bosons computed

Gauge symmetry and transformations discussed

Abstract

The noncommutative (NC) framework elaborated by Doplicher, Fredenhagen and Roberts (DFR) has a Lorentz invariant spacetime structure in order to be considered as a candidate to understand the physics of the early Universe. In DFR formalism the NC parameter ($\theta^{\mu\nu}$) is a coordinate operator in an extended Hilbert space and it has a conjugate momentum. Since $x$ and $\theta^{\mu\nu}$ are independent coordinates, the Weyl-Moyal (WM) product can be used in this framework. With these elements, in this work, we have constructed the standard electroweak model. To accomplish this task we have begun with the WM-product basis group of symmetry. After that we have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed. Finally, the gauge symmetry and gauge transformations were discussed.