We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single higher-derivative insertions we derive a closed formula that relates the perturbed one-loop counterterms to the unperturbed Schwinger-DeWitt coefficients. In the more general case, we classify the contributions to the short-distance expansion and outline a number of simplification methods. Certain difficulties of the common differential technique in the presence of higher-derivative perturbations are avoided by a systematic use of the Campbell-Baker-Hausdorff formula, which in some cases reduces the computational effort considerably.
Improved Schwinger-DeWitt techniques for higher-derivative perturbations of operator determinants / Anselmi, D; Benini, A. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1126-6708. - :10(2007).
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