Higher-derivative operators and DeWitt’s WKB ansatz

We investigate the short-distance behaviors of the higher-derivative operators appearing in some field theories which attracted much interest recently, for instance, higher-derivative quantum gravity. This study is important to find the short-distance structures of the related propagators and the one-loop divergences. We develop an algorithm which can be used to find asymptotic expansions of the heat kernels for higher-derivative operators. Our method is applicable both to flat-- and to curved--space-time cases.