Classical paths for Yang-Mills field with fixed energy

Abstract

A new classical solution for the SU(2) Yang-Mills theory, in which the Euclidean energy plays a role of a parameter is found. A correspondence between this solution and the known selfdual multi-instanton configuration, which has the topological charge N, is discussed, the number of parameters governing the new solution is found to be 8N+1. For negative energies the new solution is periodic in Euclidean time, for positive energies it exhibits the effect of localization, which states that the solution is completely described within a finite interval of time, for zero energy the found solution is reduced to a selfdual one.