FeynGrav 2.0

Abstract

We present a new version of FeynGrav. The present version supports Feynman rules for matter with non-vanishing mass and SU(N) Yang-Mills model. We revisit the gauge fixing procedure for gravity and derive interaction rules valid for an arbitrary gauge fixing parameter. We provide a few simple examples of calculations to illustrate package usage. Program summaryProgram Title: FeynGravCPC Library link to program files:https://doi.org/10.17632/rwnrbbdkkv.1Developer's repository link:github.com/BorisNLatosh/FeynGravLicensing provisions: GPLv3Programming language: Wolfram Mathematica 10 and higherExternal routines/libraries: FeynCalc [1,2]Nature of problem: FeynGrav is a software package that simplifies calculations involving the Feynman rules for gravity. These rules are complex and consist of numerous terms, but FeynGrav makes it possible to work with a specific set of rules within the FeynCalc environment. The package includes interaction rules for regular matter with different spin values, as well as for the SU(N) Yang-Mills model in curved spacetime and general relativity. FeynGrav provides scripts to generate the relevant interaction rules and libraries of pre-generated expressions, making it a powerful tool for researchers in the field of theoretical physics.Solution method: I propose a framework that provides a straightforward way to obtain expressions for the corresponding Feynman rules by efficiently utilizing perturbative expansions. In particular, within the perturbative approach to quantum gravity, certain quantities admit finite perturbative expansions, while others have infinite perturbative expansions. I derive formulas that allow the generation of terms with infinite expansions for any given order of perturbation theory. In all actions describing gravitational interactions, all derivatives can be placed on terms with finite perturbative expansions via integration by parts. In this way, the proposed framework gives a simple algorithm for deriving Feynman rules.Additional comments including restrictions and unusual features: Scripts responsible for generating interaction rules are placed in the “Rules” folder. They can be used separately and only require FeynCalc to run. The “Libs” folder contains the “FeynGravLibrariesGenerator.wl” script and the libraries it generates. “FeynGrav.wl” is the main package file that imports data from the libraries and uses it to work with the interaction rules. The file “FeynGrav_Examples.nb” contains examples of calculations.