QMeS-derivation

• Verfasst von: Pawlowski, Jan M. [VerfasserIn]
• Verfasst von: Schneider, Coralie Sophie [VerfasserIn]
• Verfasst von: Wink, Nicolas [VerfasserIn]
• Titel: QMeS-derivation
• Titelzusatz: Mathematica package for the symbolic derivation of functional equations
• Verf.angabe: Jan M. Pawlowski, Coralie S. Schneider, Nicolas Wink
• E-Jahr: 2023
• Jahr: 14 March 2023
• Umfang: 21 S.
• Fussnoten: Online verfügbar 2. März 2023, Artikelversion 14. März 2023 ; Gesehen am 20.04.2023
• Titel Quelle: Enthalten in: Computer physics communications
• Ort Quelle: Amsterdam : North Holland Publ. Co., 1969
• Jahr Quelle: 2023
• Band/Heft Quelle: 287(2023) vom: März, Artikel-ID 108711, Seite 1-21
• ISSN Quelle: 1879-2944
• DOI: doi:10.1016/j.cpc.2023.108711
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Correlation functions
• Sach-SW: Dyson-Schwinger equations
• Sach-SW: Functional equations
• Sach-SW: Functional renormalization group
• Sach-SW: Mathematica
• Sach-SW: Modified Slavnov-Taylor identities
• Sach-SW: Quantum field theory
• K10plus-PPN: 1843265117

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 summary - Program Title: QMeS-Derivation CPC Library link to program files: https://doi.org/10.17632/dzb2z4tshd.1 Developer's repository link: https://github.com/QMeS-toolbox/QMeS-Derivation Licensing provisions: GPLv3 Programming language: Mathematica Nature 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.