The Level Crossing Phenomenon with Yukawa Interactions

In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean \dop \ in three, four and five dimensions ($D$) in the presence of \tly \ nontrivial \exl \ fields. More specifically we study the cases of the \inst \ ($D=4$), \sp \ ($D=3$) as well as that of the ($D=5$) \dop \ that pertains to the existence of the \gl \ $SU(2)$ \an . We establish the \exst \ of \nl \ massive fermion \zm s in all three cases. We give closed form expressions which relate the massive with the massless \zm s. As a consequence the \lc \ phenomenon is shown to be manifest and generic in the presence of Yukawa interactions.