Semiclassical solution for Yang-Mills field with given energy

TL;DR

This paper introduces a new semiclassical solution for Yang-Mills fields parameterized by Euclidean energy, unifying instanton and sphaleron solutions, and explores its implications for tunneling processes at various temperatures.

Contribution

It presents a novel classical solution for Yang-Mills theory that generalizes instanton and sphaleron solutions using an energy parameter, enhancing understanding of tunneling mechanisms.

Findings

The solution encompasses instanton and sphaleron as special cases.

It identifies temperature ranges where tunneling is more effective with this new solution.

The solution describes tunneling with changing topological charge.

Abstract

A new classical solution for the Yang-Mills theory in which the Euclidean energy plays a role of a parameter is discussed. The instanton and sphaleron are shown to be particular examples of this more general solution. The energy parameter for them takes on special values, which are zero and sphaleron mass for the instanton and sphaleron, respectively. The solution is employed to describe the tunneling process, which is accompanied by a variation of the topological charge. A range of temperatures, where the new solution makes this tunneling more effective than the known mechanisms based on the instanton, caloron or sphaleron is found.