In theories with anomalous fermion number nonconservation, the level crossing
picture is considered a faithful representation of the fermionic quantum number
variation. It represents each created fermion by an energy level that crosses
the zero-energy line from below. If several fermions of various masses are
created, the level crossing picture contains several levels that cross the
zero-energy line and cross each other. However, we know from quantum mechanics
that the corresponding levels cannot cross if the different fermions are mixed
via some interaction potential. The simultaneous application of these two
requirements on the level behavior leads to paradoxes. For instance, a naive
interpretation of the resulting level crossing picture gives rise to charge
nonconservation. In this paper, we resolve this paradox by a precise
calculation of the transition probability, and discuss what are the
implications for the electroweak theory. In particular, the nonperturbative
transition probability is higher if top quarks are present in the initial
state.Comment: 26 pages, 6 figure
