Abstract
We formulate an effective action for averages of fields for the coupled system of scalars and (chiral) fermions. The renormalization group equations for the scale dependence of the average potential exhibit a quadratic renormalization in addition to the usual logarithmic renormalization. It is independent of the regularization scheme and the momentum cutoff. We investigate to what extent quadratic relations for the top quark mass, which were formerly based on the vanishing of the quadratic divergence, can be motivated in the light of these results.
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