On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝⁿ

Abstract

We present classification and explicit form of all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space R p,q of arbitrary finite dimension n = p + q. We use the method of hyperbolic singular value decomposition and the method of twosheeted covering of orthogonal group by spin group to do this. Nonconstant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory. 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. The results of this paper generalize our previous results for the case of arbitrary Euclidean case R n .

Classification of all constant solutions of the Yang-Mills-Dirac equations

“…In this paper, we present explicit form of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space R 1,3 . We use our previous results on the hyperbolic singular value decomposition [1] and results on constant solutions of the Yang-Mills equations with arbitrary current [2,3]. The presentation is given independently.…”