Mixing angle and Glashow's Algebra

TL;DR

This paper introduces the Glashow algebra, a new algebraic structure with a mixing angle, used to formulate a massless electroweak gauge theory, highlighting the algebra's intrinsic role in the theory's structure.

Contribution

It constructs the Glashow algebra with structure constants depending on a mixing angle and derives the electroweak Lagrangian without masses using a novel algebraic representation.

Findings

The algebra's structure constants depend on the mixing angle.

The Lagrangian is obtained using a transformed adjoint representation.

The mixing angle appears naturally in the algebraic formulation.

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.