Phi4tools Wolfram Language Paclet

Licensed under the MIT License.

Development files for the Phi4tools paclet

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(N)-symmetric model and the N-component model with cubic anisotropy. Diagrams with cubic vertices are also implemented but not computed.

The easiest way to install it is through the Wolfram Language Paclet Repository.

Plain text files for Feynman diagrams

The repository includes information about Feynman diagrams in plain text format .txt that can be found in the directory paclet/Resources. For more details on the naming conventions see the accompanying paper. The diagrams containing tadpoles are zero in the renormalization scheme considered here and are not included. The files are organized as follows:

EDGES/ Contains files describing the topology and weight factor for diagrams with up to 8 total vertices (quartic plus cubic). It also contains the files for diagrams with 9 quartic vertices (and no cubic vertices).

• Filenames are determined from the number of external legs N, the number of cubic vertices V3 and the number of quartic vertices V4 as "[N]pt[V3][V4].txt".
• Each file consists of four columns: [number of the diagram in the list], [Nickel index], [edge list], [weight factor].
• The edge list describes the lines connecting the different vertices. Internal vertices follow the same naming convention as in the Nickel index. External points are named with "e" followed by an integer.

FACTORS/ Contains files describing the symmetry (tensorial) structure for the cubic model.

• Filenames are determined from the number of external legs N, and the number of quartic vertices V4 as "cubfactorG[N]o[V4].txt".
• Each file consists of three columns: [number of the diagram in the list], [Nickel index], [symmetry factor].
• The symmetry factor is expressed in terms of the number of field components n and the ratio x = v/u between the O(n)-breaking coupling v and the O(n)-symmetric coupling u.

INTEGRANDS/ Contains files with the simplified integrands (after substitutions) and residual number of loops.

• Filenames are determined from the number of external legs N, and the number of quartic vertices V4 as "int[N]pt0[V4].txt".
• Each file consists of four columns: [number of the diagram in the list], [Nickel index], [number of independent momenta], [simplified integrand].
• The simplified integrand is expressed in terms of known "building blocks" functions (subdiagrams). External momenta are set to zero.

VALUES/ Contains files with the values of the diagrams computed at zero external momenta in three dimensions.

• Filenames are determined from the number of external legs N, and the number of quartic vertices V4 as "G[N]o[V4].txt". There are also files for the values of the derivative of the two-point function named "G2do[V4].txt".
• Each file consists of four columns: [number of the diagram in the list], [Nickel index], [value of the diagram], [uncertainty].