QMeS-Derivation: Mathematica package for the symbolic derivation of functional equations

TL;DR

QMeS-Derivation is a Mathematica package that automates the symbolic derivation of various functional equations in quantum field theory, streamlining complex calculations involving renormalisation, Dyson-Schwinger, and symmetry identities.

Contribution

It introduces a comprehensive Mathematica tool that automates the derivation, manipulation, and analysis of functional equations in quantum field theory, including truncations and momentum routing.

Findings

Automates derivation of functional equations from master equations.

Supports functional derivatives, tracing, and truncation schemes.

Includes example notebooks demonstrating its capabilities.

Abstract

We present the Mathematica package QMeS-Derivation. It derives symbolic functional equations from a given master equation. The latter include functional renormalisation group equations, Dyson-Schwinger equations, Slavnov-Taylor and Ward identities and their modifications in the presence of momentum cutoffs. The modules allow to derive the functional equations, take functional derivatives, trace over field space, apply a given truncation scheme, and do momentum routings while keeping track of prefactors and signs that arise from fermionic commutation relations. The package furthermore contains an installer as well as Mathematica notebooks with showcase examples.