Improved Schwinger-DeWitt Techniques For Higher-Derivative Corrections To Operator Determinants

We consider higher-derivative corrections to quantum gravity and quantum field theories in curved space and investigate tools to calculate the short-distance expansions of Green functions and one-loop amplitudes. 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. The common differential technique suffers from ambiguities in the presence of higher-derivative perturbations. A systematic use of the Campbell-Baker-Hausdorff formula avoids this difficulty and in some cases reduces the computational effort considerably.