Extended Weyl Symmetry

Abstract: The Abelian gauge symmetry proposed by Hermann Weyl is extended to a more general form. Afterwards the standard model is generalized to incorporate the newly defined symmetry. This symmetry extension brings new gauge particles that can be potential candidates for the dark matter. It also naturally introduces a second scalar field into the theory. The breaking of the Weyl symmetry turns this scalar field into a dimensional constant, making the Higgs as the only scalar component in the standard model. In addition to the expected benefits, there are three unexpected bonuses: (1) it brings some new understanding of the parity violation; (2) it provides an answer to the sign problem in the Higgs mechanism; (3) it gives some new perspectives on the nature of the neutrino: the extended Weyl symmetry demands that there \textit{must be} right-handed neutrino; furthermore, the smallness of the neutrino mass is protected by the extended Weyl symmetry.