Higher-order instanton effects

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Abstract
We present a formalism for calculating higher-order instanton effects based on a systematic expansion of the functional integrals about multiple instanton-anti-instanton configurations. We consider how various correlation functions may be constructed from the determinants and propagators in a background multiple-instanton field. A multiple-scattering formalism is then developed in order to express these determinants and propagators for a multi-instanton field in terms of the basic single-instanton quantities. The introduction of an improved gluon propagator based on a different choice of zero-mode constraints is required in order to justify the multiple-scattering formalism. As examples of this approach, we consider instanton interactions, which appear as corrections to the dilute-gas approximation for the instanton density, and the first-order quantum contributions to the static quark potential.