FeynGrav 4.0
Boris Latosh
TL;DR
This paper tackles the computational challenge of gravity perturbation theory by combining BRST quantization with a background geometry to yield finite ghost–graviton interactions and by adopting Cheung-Remmen variables to polynomialize the Hilbert action. The BRST approach reduces the ghost sector to a single three-point vertex and yields a straightforward generating functional for general relativity and quadratic gravity, improving both clarity and efficiency. The Cheung-Remmen formulation introduces a polynomial action with an auxiliary field and yields a finite perturbative rule set suitable for automated calculations. FeynGrav 4.0 implements these developments and adds usability enhancements, including Nieuwenhuizen operator tools and dedicated commands for Cheung-Remmen variables and higher derivative gauge fixing. This work streamlines gravity calculations and provides a scalable path toward extending to other gravity theories and optimizing performance.
Abstract
We present the new version of FeynGrav, a package that provides a set of tools to work with Feynman rules for gravity models. The new version addresses two principal issues and includes changes that improve user experience. Firstly, we present a more sophisticated implementation of the BRST formalism for general relativity and quadratic gravity, which results in a finite set of interaction rules between ghosts and gravitons. We also implement a realisation of a higher derivative gauge fixing term for quadratic gravity. Secondly, we implement Feynman rules for Cheung-Remmen variables. These variables present the general relativity action in a polynomial form and produce a finite set of Feynman rules. Lastly, we introduce some minor quality-of-life changes to the package to improve the user experience.