FERMION MODES IN INSTANTON ANTI-INSTANTON BACKGROUND IN (1+0)-DIMENSIONAL MODEL

We evaluate the eigenvalues of the Dirac operator in the background of instanton-anti-instanton configuration (I-($) over bar I), in a simple (1+0)-dimensional model, and find that quasi-zero-mode disappears for the closely localized I-T configurations. This result suggests that the configurations which are dominant at high energy in the valley method are actually non-anomalous ones and irrelevant to fermion number violation. Hence, there seems to be no theoretical basis for expecting anomalous cross section to become observable at energies of 10 TeV region in the Weinberg-Salam theory.