On a new class of non-Abelian transverse progressive waves

Annals of Physics. 2025. Vol. 480. Article 170149.

Alexander S. Rabinowitch

In the present paper, transverse progressive waves in Yang-Mills fields with SU(2) symmetry propagating in the direction of the Cartesian z-axis are considered. In this case, the considered Yang-Mills equations are reduced to a system of six nonlinear partial differential equations. Field potentials satisfying them are sought in a special form. Substituting it in the examined partial differential equations, we come to a system of three linear ordinary differential equations of the second order for complex-valued functions. Studying them, we find a new class of exact wave solutions to the Yang-Mills field equations which can describe the asymptotic behavior of the considered waves at large distances from the z-axis. When a certain condition is fulfilled, the found wave solutions exhibit an interesting property: As the coordinate increases to infinity, the nonzero field strengths change their sign an infinite number of times for fixed values of the wave phase and polar angle.

Keywords: Yang-Mills equations, SU(2) symmetry, Yang-Mills field strengths, non-Abelian progressive waves