# Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

A collection of tools for Feynman diagrams in scalar field theories

Contributed by: Giacomo Sberveglieri, Gabriele Spada

Phi4tools is an intuitive interface for visualizing, simplifying, and manipulating Feynman diagrams for the Landau-Ginzburg-Wilson theory. In more detail, it allows displaying detailed information about the diagrams, including their Nickel indices, the integrands, and numerical results. It also provides the symmetry factors for the O(Ν)-symmetric model and the Ν-component model with cubic anisotropy. Diagrams with cubic vertices are also implemented but not computed.

To install this paclet in your Wolfram Language environment,
evaluate this code:

`PacletInstall["GSberveglieri/Phi4tools"]`

To load the code after installation, evaluate this code:

`Needs["GSberveglieri`Phi4tools`"]`

Easy accessible list of Feynman diagrams

Symmetry factors for O(N) and cubic models

Automatic simplification of the diagrams via substitution of analytic subdiagrams

Tool for writing the integrands for three-dimensional theories

Results for the 0, 2, and 4-point functions of three-dimensional O(N) and cubic models up to order *λ*^{8}

Show information of a diagram, e.g. the 3^{rd} diagram of the 2-point function with 0 cubic and 3 quartic vertices:

In[1]:= |

Out[1]= |

Write symbolically the integrand for a given diagram with or without analytical substitutions and write it explicitly in the three-dimensional theory in spherical coordinates, e.g. the 3^{rd} diagram of the 2-point function with 0 cubic and 3 quartic vertices:

In[2]:= |

Out[2]= |

In[3]:= |

Out[3]= |

In[4]:= |

Out[4]= |

Visualize all the diagrams at a given order, e.g. for the 2-point function with 2 cubic and 2 quartic vertices:

In[5]:= |

Out[5]= |

Get the values for the three-dimensional theory for all the diagrams at a given order, e.g. for the 4-point function at the order *λ*^{5}:

In[6]:= |

Out[6]= |

Print the Nickel indices, e.g. those associated with the example above:

In[7]:= |

Out[7]= |

Print the symmetry factors for the O(N) model, e.g. for the 2-point function at the order *λ*^{5}:

In[8]:= |

Out[8]= |

Draw the graph for a given Nickel index:

In[9]:= |

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Vice versa:

In[10]:= |

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Wolfram Language Version 13

- 1.0.1 – 22 November 2023
- 1.0.0 – 16 October 2023