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

Russian Journal of Mathematical Physics. 2022. Vol. 29. No. 4. P. 576–580.

A. S. Rabinowitch

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 opartial 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 to this equation are represented in the form of a power series ana 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.

Keywords: recurrence relation, рекуррентное соотношение, уравнения Янга-Миллса, Yang-Mills equations, SU(2) symmetry, generalized WU-Yang form, particular exact solution, SU(2) симметрия, обобщенная форма Ву-Янга, частное точное решение