Process of fermion level crossing in the electroweak instanton

The whole process of the fermion level crossing phenomenon in the background fields of the electroweak instanton is demonstrated by numerically determining the fermion eigenvalues along Euclidean time. We assume that the fermions of a doublet are degenerate in mass and there are small-size instantons in the Weinberg-Salam model. The difference in the critical values of the Chern-Simons number at which the fermion level enters the positive and negative continuum in the level crossing process is obtained and we find that the fermion level crossing appears only in some part of the instanton configuration space