Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

GSberveglieri/ Phi4tools

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.

Installation Instructions

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`"]

Details

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 λ8

Paclet Guide

Examples

Basic Examples (8) 

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

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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 3rd diagram of the 2-point function with 0 cubic and 3 quartic vertices:

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In[4]:=
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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["GSberveglieri/Phi4tools", "GSberveglieri`Phi4tools`WriteExplicit"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][%, "Simplification" -> "Simplify"]
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]:=
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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["GSberveglieri/Phi4tools", "GSberveglieri`Phi4tools`VisualizeDiagram"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][2, 2, 2]
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 λ5:

In[6]:=
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Out[6]=

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

In[7]:=
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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["GSberveglieri/Phi4tools", "GSberveglieri`Phi4tools`NickelIndex"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][4, 0, 5]
Out[7]=

Print the symmetry factors for the O(N) model, e.g. for the 2-point function at the order λ5:

In[8]:=
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Out[8]=

Draw the graph for a given Nickel index:

In[9]:=
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Out[9]=

Vice versa:

In[10]:=
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Out[10]=

Publisher

Giacomo Sberveglieri

Disclosures

Compatibility

Wolfram Language Version 13

Version History

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

License Information

MIT License

Paclet Source

Source Metadata