FeynHelpers

FeynHelpers is a collection of interfaces that allow you to use other HEP-related tools from your FeynCalc session.

Requirements

FeynHelpers is designed as an add-on for FeynCalc. To use it you need at least FeynCalc 9.2 and Mathematica 8.

Supported tools

Tools that are currently supported are

• FIRE 5.2
• Package-X 2.1

Installation

Automatic installation

• Run the following instruction in a Kernel or Notebook session of Mathematica

  Import["https://raw.githubusercontent.com/FeynCalc/feynhelpers/master/install.m"]
  InstallFeynHelpers[]
  

  If the above code fails with URLFetch::invhttp: SSL connect error (e.g. on Mathematica 9 under OS X), try

  ImportString[URLFetch["https://raw.githubusercontent.com/FeynCalc/feynhelpers/master/install.m"]]
  InstallFeynHelpers[]
  

• The automatic installer can also install Package-X and FIRE for you. It will offer you this possiblity at the end of the installation process

Manual installation

• Create a directory FeynHelpers inside

   FileNameJoin[{$UserBaseDirectory, "Applications", "FeynCalc", "AddOns"}]
  

  and put the source code there.

• Install Package-X and FIRE packages. It should be possible to load Package-X via

   <<X`
  

  and FIRE via

   << FIRE5`
  

Development version

If you like the bleeding edge and you are already using the development version of FeynCalc, you can also install the development version of FeynHelpers

Import["https://raw.githubusercontent.com/FeynCalc/feynhelpers/master/install.m"]
InstallFeynHelpers[InstallFeynHelpersDevelopmentVersion->True]

Experimental Fermat interface

The development version features an interface to the CAS Fermat by R. Lewis. At the moment the main function of this interface is FerSolve, which employs Fermat to solve systems of linear equations. Notice that to run FerSolve you need to download the Fermat binary and put ferl6 (Linux) or ferm6 (macOS) to FileNameJoin[{$FeynHelpersDirectory, "ExternalTools", "Fermat"}].

Some examples for running FerSolve would be

FerSolve[{a x + y == 7, b x - y == 1}, {x, y}]

FerSolve[{2 x + y c == 2, 4 x == c}, {x, y}]

eqs = {M0 == (1 - f1 - f2 - f3 - f4 - f5 - f6 - f7 - f8 - f9 - f10 - 
      f11 - f12 - f13 - f14 - f15 - f16)*m0, 
  M1 == f1*m0 + (1 - f1 - f2 - f3 - f4 - f5 - f6 - f7 - f8 - f9 - 
       f10 - f11 - f12 - f13 - f14 - f15 - f16)*m1, 
  M2 == f1*m1 + 
    f2*m0 + (1 - f1 - f2 - f3 - f4 - f5 - f6 - f7 - f8 - f9 - f10 - 
       f11 - f12 - f13 - f14 - f15 - f16)*m2, 
  M4 == f1*m3 + f2*m2 + f3*m1 + f4*m0, 
  M5 == f2*m3 + f3*m2 + f4*m1 + f5*m0, 
  M6 == f3*m3 + f4*m2 + f5*m1 + f6*m0, 
  M7 == f4*m3 + f5*m2 + f6*m1 + f7*m0, 
  M8 == f5*m3 + f6*m2 + f7*m1 + f8*m0, 
  M9 == f6*m3 + f7*m2 + f8*m1 + f9*m0, 
  M10 == f7*m3 + f8*m2 + f9*m1 + f10*m0, 
  M11 == f8*m3 + f9*m2 + f10*m1 + f11*m0, 
  M12 == f9*m3 + f10*m2 + f11*m1 + f12*m0, 
  M13 == f10*m3 + f11*m2 + f12*m1 + f13*m0, 
  M14 == f11*m3 + f12*m2 + f13*m1 + f14*m0, 
  M15 == f12*m3 + f13*m2 + f14*m1 + f15*m0, 
  M16 == f13*m3 + f14*m2 + f15*m1 + f16*m0};
vars = {f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12, f13, f14, 
  f15, f16}
FerSolve[eqs, vars]

FerSolve can be also employed for calculating new tensor reduction with Tdec. For example,

$LoadAddOns = {"FeynHelpers"};
<< FeynCalc`

Tdec[{{p1, mu1}, {p1, mu2}, {p1, mu3}, {p1, mu4}, {p2, mu5}, {p2, 
   mu6}}, {Q1, Q2}, Solve -> FerSolve, UseTIDL -> False, 
 FCVerbose -> 1]

Experimental QGRAF interface

The interface to QGRAF is still very unstable and full of bugs and missing features. Just to give a general idea of how it is supposed to work, here is a simple QED 2-loop example

SetDirectory[NotebookDirectory[]];
QGLoadInsertions[];
out = QGCreateAmp[2, {"El[p]"} -> {"El[p]"}, QGLoopMomentum -> l, 
  QGModel -> "QEDOneFlavor", QGShowOutput -> False]
  
QGConvertToFC[out[[1]], DiracChainJoin -> True]  

QGPrepareDiagramsTeX[out[[2]], "dias.tex"]
(*or QGPrepareDiagramsTeX[out[[2]], "Dias", Split -> True] *)

Usage

For usage information see the accompanying paper arXiv:1611.06793 and the supplied examples.

Acknowledgments

If you use FeynHelpers in you work, please cite

• V. Shtabovenko, "FeynHelpers: Connecting FeynCalc to FIRE and Package-X", Comput. Phys. Commun., 218, 48-65, 2017, arXiv:1611.06793

Also don't forget to cite the authors of the tools that you are calling from FeynHelpers, which are

• FIRE if you use FIREBurn
• Package X if you use PaXEvaluate
• Fermat if you use FerSolve

License

• The code of FeynHelpers is covered by the GNU General Public License 3.
• This does not apply to the packages for which FeynHelpers provides an interface to FeynCalc. For the licensing of those packages please check the informations provided by the respective authors.