Mixing angle and Glashow's Algebra

Abstract

Considering transformations in the basis of fundamental fields on a principal fiber bundle, without modification in the space-time sector, we construct an algebra GA, which we call Glashow algebra. The structure constants of this algebra depend on a mixing angle. The Lagrangian of the gauge theory of electroweak interactions without masses is obtained using a representation of GA which is the transformed of the adjoint representation of the direct product of SU(2) and U(1), and does not coincide with the adjoint representation of GA. The mixing angle is automatically present in the theory if GA is used.