Some mathematical considerations about generalized Yang-Mills theories

TL;DR

This paper explores generalized Yang-Mills theories that incorporate non-vector gauge fields, providing their geometric interpretation and discussing applications to the Standard Model, with insights into their mathematical and physical implications.

Contribution

It introduces a framework for generalized Yang-Mills theories with non-vector gauge fields and analyzes their geometric structure and potential applications.

Findings

Generalized gauge fields beyond vectors are mathematically consistent.

Geometric interpretation of these theories is developed.

Application to the Glashow-Weinberg-Salam model is discussed.

Abstract

Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related mathematical and physical considerations are made.