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

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.