On the Propagation of Local Perturbations in Yang–Mills Fields with $SU(2)$ Symmetry

Abstract

In the present paper, the classical Yang–Mills equations with $SU$(2) symmetry are considered. The application of a generalized Wu–Yang form for field potentials results in a nonlinear differential equation of the second order. This equation is studied for a Yang–Mills field generated by a point-like source acting at the instant $t=0$. In the examined case, the considered partial differential equation is reduced to a nonlinear ordinary differential equation of the second order for a function of the dimensionless argument $r/(ct)$, where $r$ is the distance from the field source and $t>0$ is time. The desired solutions of this equation are represented in the form of a power series and a recurrence relation for its coefficients is obtained. In a limiting case, an exact solution to the examined differential equation is found. This solution is applied to obtain a condition of convergence of the considered power series.