One-loop divergences in theories with an arbitrary nonminimal operator in curved space (Q1280834)

The explicit expression for the one-loop effective action in the theory with an arbitary differential operator is developed. It is shown how to calculate the divergent part of the effective action with the help of the Feynman diagram technique. The results for flat space are repeated and generalized to the case of a Riemannian manifold, with regard to which all possible diagrams for both cases are considered. In the general case, a weak field approximation is used for minimal and nonminimal operators. Finally, the covariant results are obtained from the weak field approximation. Some particular cases are discussed.