The Level Crossing Phenomenon with Yukawa Interactions

In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean Dirac operator in three, four and five dimensions (D) in the presence of topologically nontrivial external fields. More specifically we study the cases of the instanton (D = 4), sphaleron (D = 3) as well as that of the (D = 5) Dirac operator that pertains to the existence of the global SU(2) anomaly. We establish the existence of normalizable massive fermion zero modes in all three cases. We give closed form expressions which relate the massive with the massless zero modes. As a consequence the level crossing phenomenon is shown to be manifest and generic in the presence of Yukawa interactions. e-mail:[email protected] e-mail:[email protected] e-mail:[email protected]