In this paper, we present all constant solutions of the Yang-Mills equations
with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current
in Euclidean space ${\mathbb R}^n$ of arbitrary finite dimension $n$. Namely,
we obtain all solutions of the special system of $3n$ cubic equations with $3n$
unknowns and $3n$ parameters. Using the invariance of the Yang-Mills equations
under the orthogonal transformations of coordinates and gauge invariance, we
choose a specific system of coordinates and a specific gauge fixing for each
constant current and obtain all constant solutions of the Yang-Mills equations
in this system of coordinates with this gauge fixing, and then in the original
system of coordinates with the original gauge fixing. We use the singular value
decomposition method and the method of two-sheeted covering of orthogonal group
by spin group to do this. We prove that the number ($0$, $1$, or $2$) of
constant solutions of the Yang-Mills equations in terms of the strength of the
Yang-Mills field depends on the singular values of the matrix of current. The
explicit form of all solutions and the invariant $F^2$ can always be written
using singular values of this matrix. Nonconstant solutions of the Yang-Mills
equations can be considered in the form of series of perturbation theory. The
relevance of the study is explained by the fact that the Yang-Mills equations
describe electroweak interactions in the case of the Lie group ${\rm SU}(2)$.
The results of this paper are new and can be used to solve some problems in
particle physics, in particular, to describe physical vacuum and to fully
understand a quantum gauge theory.