Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space ℝp,q

Abstract

We present a classification and an explicit form of all constant solutions of the Yang–Mills equations with [Formula: see text] gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space [Formula: see text] of arbitrary finite dimension [Formula: see text]. 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 [Formula: see text] cubic equations with [Formula: see text] unknowns and [Formula: see text] 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.