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arXiv · 1912.04996

Classification of all constant solutions of ${\rm SU}(2)$ Yang-Mills equations with arbitrary current in pseudo-Euclidean space ${\mathbb R}^{p,q}$

D. S. Shirokov
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Abstract

We present a classification and an explicit form of all constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ${\mathbb R}^{p,q}$ of arbitrary finite dimension $n=p+q$. Using hyperbolic singular value decomposition and two-sheeted covering of orthogonal group by spin group, we solve the nontrivial system for constant solutions of the Yang-Mills equations of $3n$ cubic equations with $3n$ unknowns and $3n$ parameters in the general case. We present a new symmetry of this system of equations. All solutions in terms of the potential, strength, and invariant of the Yang-Mills field are presented. Nonconstant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory using all constant solutions as a zeroth approximation.

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D. S. Shirokov. 2019-12-10. Classification of all constant solutions of ${\rm SU}(2)$ Yang-Mills equations with arbitrary current in pseudo-Euclidean space ${\mathbb R}^{p,q}$. https://doi.org/10.1142/s0217732323500967

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