# On the Higgs mechanism in $U(1)\times U(2)\times U(3)$ gauge group as a base for noncommutative standard model

## TL;DR

This paper investigates the Higgs mechanism within a noncommutative space-time framework for the gauge group U(1)×U(2)×U(3), revealing that the Goldstone boson equivalence theorem does not hold due to symmetry reduction constraints.

## Contribution

It demonstrates that the symmetry reduction mechanisms in noncommutative space-time conflict with the electroweak Higgs mechanism, violating the Goldstone boson equivalence theorem.

## Key findings

- Goldstone boson equivalence theorem is violated
- Symmetry reduction mechanisms are incompatible with the Higgs mechanism
- Standard model gauge group can be transcribed to NC space-time with constraints

## Abstract

Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on $U(3)\times U(2)\times U(1)$ can be transcribed to NC space-time consistently with these constraints \cite{nNCSM}. In fact, through two new symmetry reduction mechanisms, this gauge group is reduced to the usual standard model one. In this paper, we show that, on the contrary to the usual standard model, the Goldestone boson equivalence theorem is violated due to the incompatibility of the new symmetry reduction mechanisms with the electroweak Higgs mechanism.