One-loop counterterms for the dimensional regularization of arbitrary Lagrangians

TL;DR

This paper provides universal formulas for calculating one-loop divergences in quantum field theories with arbitrary operators in curved spacetime, simplifying complex calculations into algebraic procedures.

Contribution

It introduces master formulas that serve as algorithms for one-loop divergence calculations for any operator order in 4D curved space.

Findings

Formulas applicable to minimal and nonminimal operators

Implementation demonstrated using REDUCE system

Simplifies one-loop divergence computations

Abstract

We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms, because the one-loop calculations are then reduced to the simplest algebraic operations. Some test applications are considered by REDUCE analytical calculation system.