DoFun 3.0: Functional equations in mathematica

Abstract

We present version 3.0 of the Mathematica package DoFun for the derivation of functional equations. In this version, the derivation of equations for correlation functions of composite operators was added. In the update, the general workflow was slightly modified taking into account experience with the previous version. In addition, various tools were included to improve the usage experience and the code was partially restructure for easier maintenance. .70.+k,11.15.Tk Nature of problem: Derivation of functional renormalization group equations, Dyson-Schwinger equations and equations for correlations functions of composite operators in symbolic form which can be translated into algebraic form. Solution method: Implementation of algorithms for the derivations of these equations and tools to transform the symbolic to the algebraic form. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. The output is compatible with the syntax of many other programs and is therefore suitable for further (algebraic) computations.

Higher spin glueballs from functional methods

“…The derivation is fully worked out for a similar example in Ref. [26] and can also be done algorithmically with a computer [27]. O 1 can be split into contributions with two, three, and four gluon fields, and one can group their contributions to D(P) accordingly into terms with four, five, …, eight gluon fields.…”

The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models

“…To evaluate the flow of RG-equations presented in this work we use self-written the Mathematica codes based on the packages xAct [173][174][175], DoFun [176,177], FormTracer [178] and Package-X [179].…”

Dense two-color QCD from Dyson-Schwinger equations

“…HPC Clusters at the University of Graz were used for the numerical computations. The software programs and packages Mathematica [95], DoFun [96][97][98] and CrasyDSE [99] were used for deriving and solving numerically the DSEs. Feynman diagrams were created with Jaxodraw [100].…”