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
R1,3 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.Comment: 19 page