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We discuss the derivation of the trace anomaly using a non-local effectiveaction at one loop. This provides a simple and instructive form and emphasizesinfrared physics. We then use this example to explore several of the propertiesof non-local actions, including displaying the action for the full non-localenergy-momentum tensor. As an application, we show that the long-distancecorrections at one loop lead to quantum violations of some classicalconsequences of the equivalence principle, for example producing a frequencydependence of the gravitational bending of light.

QED trace anomaly, non-local Lagrangians and quantum Equivalence Principle violations