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Abstract
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.
Highlights
The invariance of the action leads to the tracelessness of the energy momentum tensor
We show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light
Rescaling the gauge field by the bare electric charge Aμ → Aμ/e0, we can write a one-loop effective action describing both of these effects
Summary
We give a brief derivation of the non-local effective action using the background field method. The classical action for QED coupled to a charged field reads. The one loop effective action is obtained by integrating out the charged scalar field. Integrating by parts to place the derivatives on the propagators and noting that the latter is a function of the geodesic distance |x−y|, we find the order-A2 contribution i. Converting one x-derivative back to one with respect to y and integrating by parts we convert the result to a manifestly gauge invariant form dDxdDy Fμν (x). It is easy to renormalize the electric charge and express the 4D effective action in a quasi-local form
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