Higher-derivative operators and DeWitt’s WKB ansatz

Abstract

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.

Momentum-space representation of Green’s functions with modified dispersion on ultrastatic space-time

“…When ǫ = 0, the ansatz (30) simply does not work, and the reason will be clear at the end of next section (see also [10]). As our n-dimensional problem can be seen as the Euclidean continuation of a n-dimensional theory with a 2 term, one can find the heat kernel by the method presented in [15]. However, as we will see in the next section, there is an alternative route, which simplifies the calculations and keep track closely of the physics behind the mathematical structure.…”

One-loop counterterms for the dimensional regularization of arbitrary Lagrangians

“…This approach was successfully applied to obtain one-loop counterterms in theories with the simplest second and forth order operators D i j . We should also mention other covariant methods, that in principle allow to get the divergent part of effective action [4,5,6].…”

“…In Sec. 4 we describe a method for the derivation of a master formula for an arbitrary nonminimal operator on the curved background and present the result.…”