AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic tripl ets coupled to a gauge field on a circle. Because the fundamental grou p is non-trivial, pi1(O(3)) = Z2, fermionic level crossing - circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operato r under continuous external field transformations. They are shown to b e related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We a rgue that fermionic degrees of freedom in the presence of an infinitel y large external field violate perturbative decoupling.