  We study a series of the Wess-Zumino actions obtained by repeatedly
integrating conformal anomalies with respect to the conformal-factor field that
appear at higher loops. We show that they arise as physical quantities required
to make nonlocal loop correction terms diffeomorphism invariant. Specifically,
in a conformally flat spacetime $ds^2=e^{2\phi}(-d\eta^2 + d{\bf x}^2)$, we
find that effective actions are described in terms of momentum squared
expressed as a physical $Q^2 = q^2/e^{2\phi}$ for $q^2$ measured by the flat
metric, which recalls the relationship between physical momentum and comoving
momentum in cosmology. It is confirmed by calculating the effective action of
QED in such a curved spacetime at the 3-loop level using dimensional
regularization. The same applies to the case of QCD, in which we show that the
effective action can be summarized in the form of the reciprocal of a running
coupling constant squared described by the physical momentum. We also see that
the same holds for renormalizable quantum conformal gravity and that conformal
anomalies are indispensable for formulating the theory.
