A possibility on prohibition of Higgs mass by the extended Lorentz transformation in noncommutative geometry

TL;DR

This paper introduces an extended Lorentz transformation within noncommutative geometry that could potentially prohibit the Higgs mass, by ensuring invariance of the bosonic Lagrangian through transformations of differential two-forms.

Contribution

It proposes a novel extended Lorentz transformation in noncommutative geometry that maintains bosonic Lagrangian invariance and suggests a mechanism to prohibit the Higgs mass.

Findings

Transformation preserves bosonic Lagrangian invariance.

Links two-form transformations to product field transformations.

Provides a new symmetry framework potentially forbidding Higgs mass.

Abstract

In this letter, we propose the extended Lorentz transformation in noncommutative geometry, as a possibility on prohibition of the Higgs mass. Since it is difficult to build the symmetry between the connections $A_{\mu}$ and $H$, the transformation is defined for the differential two-forms. The parameter of the transformation $\omega$ changes a two-form into other two-forms. Comparing the coefficients of the two-forms, the transformations are translated to those of the product fields $F_{\mu\nu}, D_{\mu} H$ and $HH^{\dagger}$. It shows the invariance of the bosonic Lagrangian explicitly.