Tutorial 3: Code generation from Mathematica and Extractors

This tutorial describes, how to generate flow equations from Mathematica and use them in the c-Code.

Generation of Flow equations

First, one has to import the DiFfRG package and set the current directory.

Get["DiFfRG`"]
SetDirectory[GetDirectory[]];

The GetDirectory[] command returns the directory of the current notebook of wolfram script. DiFfRG imports, besides its own libraries, the packages FormTracer and QMeSderivation, which are used for the diagramatic derivation of the flow equations. The method works as folows:

1. Use QMeSderivation to derive a diagramatic description of the 1PI-n-Point Functions
2. Insert the propagators in the flow equations
3. Compute the \(STr\) with FormTracer
4. Export the flow equations ()

1. QMeSderivation

This will just quickly recap the process, to derive the diagramatic expressions, a more detailed version can be found here. First, one has to define the Master-Equation

fRGEq = {
   "Prefactor" -> {1/2},
   <|"type" -> "Regulatordot", "indices" -> {i, j}|>,
   <|"type" -> "Propagator", "indices" -> {i, j}|>
   };

After that, one defines the structure of the model

fields = <|"bosonic" -> {\[Sigma][p], \[CapitalPi][p, {a}]},
 
   "fermionic" -> {{qb[p, {d, c, f}], q[p, {d, c, f}]}}|>;
 
Truncation = {{\[Sigma], \[Sigma]}, {\[CapitalPi], \[CapitalPi]}, {q,
    qb},(* propagators *)
   {qb, q, \[Sigma]}, {qb, q, \[CapitalPi]}, {qb,
    q, \[Sigma], \[Sigma]}, {qb, q, \[CapitalPi], \[CapitalPi]}, {qb,
    q, \[Sigma], \[CapitalPi]}, {qb,
    q, \[Sigma], \[Sigma], \[Sigma]}, {qb,
    q, \[Sigma], \[Sigma], \[CapitalPi]}, {qb,
    q, \[Sigma], \[CapitalPi], \[CapitalPi]}, {qb,
    q, \[CapitalPi], \[CapitalPi], \[CapitalPi]}, (* quark-
   meson scatterings *)
    {\[Sigma], \[Sigma], \[Sigma]}, {\[Sigma], \[CapitalPi], \
\[CapitalPi]}, {\[Sigma], \[Sigma], \[Sigma], \[Sigma]}, {\[Sigma], \
\[Sigma], \[CapitalPi], \[CapitalPi]}, {\[CapitalPi], \[CapitalPi], \
\[CapitalPi], \[CapitalPi]}(* meson scatterings *)
   };
 
SetupfRG = <|"MasterEquation" -> fRGEq,
   "FieldSpace" -> fields,
   "Truncation" -> Truncation|>;