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

In this letter, we propose the extended Lorentz transformation in noncommutative geometry, as a possibility on protection of the Higgs mass. In order to reconcile this transformation with the noncommutative differential geometry, we introduce the doubled matrix which describe the differential forms. This formulation of matrix clearly shows the invariance of the bosonic Lagrangian under the transformation. For the Dirac Lagrangian, the appropriate matrix representation of this transformation is not be found. Instead of that, we suggest a symmetry-like operator $\hat \gamma^{M}$ whose action is defined by the commutation relation, $\hat \gamma^{M} X = [\gamma^{M} , X]$.