Corrections to high-energy particles interacting through an instanton as quantum fluctuations in the position of the instanton

We study the corrections to hard-particle interactions mediated by an instanton through quantum fluctuations around the instanton field. We show that the sum of corrections can be understood as quantum fluctuations in the local translation of the instanton as seen by the high-energy particles. In the massless O(3) model in 1+1 dimensions, we demonstrate a systematic way to evaluate such corrections. In this model, we prove that the corrections have the form exp[F(E)/], for large negative values of s. The quantity F(±E) may be evaluted by solving a classical theory for a local field which measures the deviation of fields from the position of the instanton. This field is defined by the relation (x)=inst(x+(x)) where inst is the classical instanton field. For large positive values of s and for ±2s21, we cannot compute the corrections in any systematic expansion, but nevertheless under relatively weak assumptions about the behavior of the -field correlation function, it appears that the corrections are not exponentially suppressed in s.