Classical paths for Yang-Mills field with fixed energy

TL;DR

This paper introduces a new classical solution for SU(2) Yang-Mills theory parameterized by Euclidean energy, revealing different behaviors such as periodicity and localization, and connecting to known instanton solutions.

Contribution

It presents a novel classical solution in SU(2) Yang-Mills theory with a parameterized energy, expanding understanding of solution space and its relation to instantons.

Findings

Solution depends on Euclidean energy parameter

For negative energy, the solution is periodic in Euclidean time

For zero energy, the solution reduces to a selfdual instanton

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.