On constant solutions of SU(2) Yang-Mills-Dirac equations

Abstract: For the first time, a complete classification of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space ${\mathbb R}^{1,3}$ is given. The explicit form of all solutions is presented. We use the method of hyperbolic singular value decomposition of real and complex matrices and the two-sheeted covering of the group SO(3) by the group SU(2). In the degenerate case of zero potential, we use the pseudo-unitary symmetry of the Dirac equation. Nonconstant solutions can be considered in the form of series of perturbation theory using constant solutions as a zeroth approximation; the equations for the first approximation in the expansion are written.