Infrared problems in the presence of instantons

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Abstract
In theories without an intrinsic mass scale, the semiclassical approximation may yield erroneous results. A concrete example is provided by a flat-bottom potential in one dimension. This massless model is discussed in detail and compared to a model which has a mass scale. Both models have finite-action instantons. Nevertheless only in the massive case does instanton physics lead to the correct results. Since quantum chromodynamics is a massless theory, infrared divergences may occur while quantizing it around the instanton; this possibility is discussed.