Some aspects of instantons

Abstract

We study various effects associated with Euclidean instanton solutions. By means of an instructive example, we discuss how the probability of tunnelling among vacuum states in Minkowski space is connected with stationary (instanton) solutions in Euclidean space. Next we examine the cluster decomposition properties of non-Abelian gauge theories and indicate how these are recovered in the presence of instanton solutions. The validity of perturbation theory in these field theories is discussed. We show that perturbative analyses are only tenable in the deep Euclidean region, unless there is an intrinsic scale. Finally, we examine the role that instantons have in providing violations of otherwise conserved quantum numbers. We study, in particular, how fermion number nonconservation results by a careful examination of the path integral for the fermion-generating functional.