Equivariant Connections and their applications to Yang-Mills equations

TL;DR

This paper introduces the concept of equivariant connections to simplify Yang-Mills equations for specific gauge groups, enabling modeling of fundamental interactions through nonlinear differential equations.

Contribution

It develops the theory of $SO^+(p,q)$-equivariant connections to reduce complex Yang-Mills equations for various gauge groups, facilitating applications in particle physics.

Findings

Reduced Yang-Mills equations to nonlinear differential equations

Modeled electroweak and strong interactions using these equations

Provided a new framework for analyzing gauge theories with symmetry considerations

Abstract

We reduce Yang-Mills equations for $SO^+(p,q)$, $Spin^+(p,q)$ and $SU(n)$ bundles, with constant and isotropic metrics, by developing the concept of $SO^+(p,q)$-equivariance. This allows us to model the electroweak interaction and $SO^+(p,q)$ bundles with a non-linear second order differential equation as well as the weak and strong interaction with a non-linear wave equation.