An introduction to generalized Yang-Mills theories

TL;DR

This paper introduces generalized Yang-Mills theories where scalar fields are gauged similarly to vector fields, simplifying the theory's structure and exploring examples like the Standard Model and grand unification.

Contribution

It defines generalized Yang-Mills theories using a minimal set of terms and representations, extending traditional theories with a focus on their construction and examples.

Findings

Simplified Lagrangian with only two terms and two irreducible representations.

Application to the Glashow-Weinberg-Salam model and SU(5) grand unification.

Discussion on five-dimensional formalism and critical comments.

Abstract

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A physical theory using Yang-Mills theories requires several terms and irreducible representations, but with generalized Yang-Mills theories, only two terms and two irreducible representations are required. These theories are constructed based upon the maximal subgroups of the gauge Lie group. The two terms of the lagrangian are the kinetic energy of fermions and of bosons. A brief review of Yang-Mills theories and covariant derivatives is given, then generalized Yang-Mills theories are defined through a generalization of the covariant derivative. Two examples are given, one pertaining the Glashow-Weinberg-Salam model and another SU(5) grand unification. The first is based upon a $U(3)\supset U(1)\times U(1)\times SU(2)$ generalized Yang-Mills theory, and the second upon a $SU(6)\supset U(1)\times SU(5)$ theory. The possibility of expressing generalized Yang-Mills theories using a five-dimensional formalism is also studied. The situation is unclear in this case. At the end a list of comments and criticisms is given.