THE LEVEL-CROSSING PHENOMENON WITH YUKAWA INTERACTIONS

In the minimal model of electroweak interactions we carefully investig ate the spectrum of the massive euclidean Dirac operator in three, fou r and five dimensions (D) in the presence of topologically non-trivial external fields. More specifically we study the cases of the instanto n (D = 4), sphaleron (D = 3) as well as that of the (D = 5) Dirac oper ator that pertains to the existence of the global SU(2) anomaly. We es tablish the existence of normalizable massive fermion zero modes in al l three cases. We give closed form expressions which relate the massiv e with the massless zero modes. As a consequence the level crossing ph enomenon is shown to be manifest and generic in the presence of Yukawa interactions.