Examples of the Vilkovisky-Dewitt effective action in one-loop quantum gravity

We present two examples where the contribution of one-loop gravitons to the renormalized stress-energy tensor may be calculated explicitly from both the standard and the Vilkovisky-DeWitt effective action. The renormalization is carried out using the Hadamard renormalization procedure outlined by Allen, Folacci, and Ottewill [Phys. Rev. D 38, 1069 (1988)]. The examples show that the standard and Vilkovisky-DeWitt formulations of quantum field theory lead to different physical predictions at one loop