The presence of gravity generalizes the notion of scale invariance to Weyl
invariance, namely, invariance under local rescalings of the metric. In this
work, we have computed the Weyl anomaly for various classically scale or Weyl
invariant theories, making particular emphasis on the differences that arise
when gravity is taken as a dynamical fluctuation instead of as a non-dynamical
background field. We find that the value of the anomaly for the Weyl invariant
coupling of scalar fields to gravity is sensitive to the dynamical character of
the gravitational field, even when computed in constant curvature backgrounds.
We also discuss to what extent those effects are potentially observable.Comment: 37 pages, 1 tabl