Gauge representations of the Lorentz group and classical solutions of the Yang-Mills equation

The notion of gauge representation of the Lorentz group is introduced. For these representations the Lorentz transformations of the Yang-Mills potentials are accompanied by suitable gauge transformations satisfying certain conditions. In the case of gauge group SU(2), solutions of these conditions are found. Solutions of the invariance equations for the gauge potentials which are defined inside the light cone are also found. For the invariant potentials the Yang-Mills equation reduces to one nonlinear differential equation for one variable whose solutions are expressed in terms of Jacobi elliptic functions