Equivariant Connections and their applications to Yang-Mills equations

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