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

Abstract

We present the Mathematica package QMeS-Derivation, available on GitHub. 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. Program summaryProgram Title: QMeS-DerivationCPC Library link to program files:https://doi.org/10.17632/dzb2z4tshd.1Developer's repository link:https://github.com/QMeS-toolbox/QMeS-DerivationLicensing provisions: GPLv3Programming language: MathematicaNature of problem: Deriving symbolic functional equations starting from a quantum master equation.Solution method: Taking functional derivatives of the modified Slavnov-Taylor identities, the Dyson-Schwinger, functional renormalisation group equation or user defined master equations, taking the trace in field space and applying a truncation, doing a momentum routing for one-loop diagrams.Additional comments including restrictions and unusual features: QMeS operates theory independent and is based on a small number of rules, i.e. the (anti-)commutation relation of (fermions)bosons and general functional derivative rules.