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In this paper, we present all constant solutions of the Yang-Mills equationswith ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian currentin Euclidean space ${\mathbb R}^n$ of arbitrary finite dimension $n$. Using theinvariance of the Yang-Mills equations under the orthogonal transformations ofcoordinates and gauge invariance, we choose a specific system of coordinatesand a specific gauge fixing for each constant current and obtain all constantsolutions of the Yang-Mills equations in this system of coordinates with thisgauge fixing, and then in the original system of coordinates with the originalgauge fixing. We use the singular value decomposition method and the method oftwo-sheeted covering of orthogonal group by spin group to do this. We provethat the number (0, 1, or 2) of constant solutions of the Yang-Mills equationsin terms of the strength of the Yang-Mills field depends on the singular valuesof 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. The relevanceof the study is explained by the fact that the Yang-Mills equations describeelectroweak interactions in the case of the Lie group ${\rm SU}(2)$.Nonconstant solutions of the Yang-Mills equations can be considered in the formof series of perturbation theory. The results of this paper are new and can beused to solve some problems in particle physics, in particular, to describephysical vacuum and to fully understand a quantum gauge theory.

On constant solutions of ${\rm SU}(2)$ Yang-Mills equations with arbitrary current in Euclidean space ${\mathbb R}^n$