Semi-automatic Calculations of Multi-loop Feynman Amplitudes with AmpRed

TL;DR

AmpRed is a Mathematica package that streamlines the semi-automatic calculation of complex multi-loop Feynman amplitudes using advanced mathematical methods, enhancing efficiency and flexibility in high-energy physics computations.

Contribution

It introduces a versatile Mathematica tool that implements integration by parts and differential equations for general parametric integrals in multi-loop Feynman calculations.

Findings

Efficient semi-automatic calculation of multi-loop Feynman amplitudes.

Supports general parametric integrals beyond momentum-space.

Includes tools for differential equations and tensor algebra handling.

Abstract

We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the Feynman-parameter representation. It allows for the calculations of general parametric integrals (which may not have momentum-space correspondences). Various user-friendly tools for multi-loop calculations, such as those to construct and solve differential equations for Feynman integrals, are provided. It can also deal with tensor algebras in non-relativistic field theories. Interfaces to some packages, like QGRAF and FORM, are also provided.