Instantons in unusual settings

Abstract

Instantons may still be an important feature of a quantum system even if they are not exact solutions of the classical equations. This is illustrated in a simple quantum mechanics problem and in non-abelian gauge theories coupled to scalars. In this latter case, it is shown that under certain circumstances, instantons may cause the scalars to be in a symmetric phase even if their perturbative mass is negative or in a broken symmetric phase even if the mass is positive. We also discuss the application of our methodology to the case of QCD merons in a background instanton gas.