Feynman

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Feynman

The package Feynman generate the Feynman integrand associated to a Feynman diagram (graph) and compute an IBP system using the module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. In the future, it might provide an interface to utilize the packages NeatIBP, pfd-parallel and further software for improved performance, and to solve, in addition to the internal functionality, the row reduction problem. The package Feynman is based on the computer algebra system OSCAR and is provided as a package for the Julia programming language.

This package can generate the Feynman integrand associated to a Feynman graph $G$ if $\text{number of internal edges} < \frac{1}{2}l(l+1)+el$. Here $l$ is the loop number and $e=span<p_1,...,p_{n_{ext}}>$ is the number of linearly independent external momenta of $G$. In the generic case (That we considered in this package), $e=p_{n_{ext}}-1$.

In the case $\text{number of internal edges} < \frac{1}{2}l(l+1)+el$, the package generate the Feynman integrand associated to a larger Feynman graph $G'$ so that $G$ is a subgraph of $G'$. User can set appropriately the denomiator powers to zero to obtain the Baikov representation of $G$.

Installation

We assume that Julia is installed in a recent enough version to run OSCAR. Navigate in a terminal to the folder where you want to install the package and pull the package from Github:

git pull https://github.com/singular-gpispace/Feynman.git

In the same folder execute the following command:

julia --project

This will activate the environment for our package. In Julia install missing packages:

import Pkg; Pkg.instantiate()

and load our package. On the first run this may take some time.

using Feynman