A note about the t`Hooft`s ansatz for SU(N) real time guage theories

Abstract

The t`Hooft's ansatz reduces the classical Yang--Mills theory to the $\lambda {\varphi }^4$ one. It is shown that in the frame of this ansatz the real-time classical solutions for the arbitrary SU(N) gauge group is obtained by embedding $SU(2)\times SU(2)$ into SU(N). It is argued that this group structure is the only possibility in the frame of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown.