Equivariant Connections and their applications to Yang-Mills equations

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.