PUB - Publikationen an der Universität Bielefeld

In theories with anomalous fermion number nonconservation, the level crossingpicture is considered a faithful representation of the fermionic quantum numbervariation. It represents each created fermion by an energy level that crossesthe zero-energy line from below. If several fermions of various masses arecreated, the level crossing picture contains several levels that cross thezero-energy line and cross each other. However, we know from quantum mechanicsthat the corresponding levels cannot cross if the different fermions are mixedvia some interaction potential. The simultaneous application of these tworequirements on the level behavior leads to paradoxes. For instance, a naiveinterpretation of the resulting level crossing picture gives rise to chargenonconservation. In this paper, we resolve this paradox by a precisecalculation of the transition probability, and discuss what are theimplications for the electroweak theory. In particular, the nonperturbativetransition probability is higher if top quarks are present in the initialstate.