Feynman rules

Matchete can automatically derive momentum-space Feynman rules from any Lagrangian written in Matchete’s notation. This is useful for analytical cross-checks, amplitude computations, or as a preparatory step for the UFO export.

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Usage

FeynmanRules takes a Lagrangian and returns all interaction vertices:

vertices = FeynmanRules[L];

To compute the Feynman rule for a single vertex, pass the external field labels as the second argument:

(* three-gluon vertex *)
FeynmanRules[L, {G, G, G}];

Use Bar or Conj for conjugated fields in the list (e.g., {Bar@psi, psi, phi} for a Yukawa-type vertex).

The Legs option restricts the computation by vertex size rather than field content:

FeynmanRules[L, Legs -> 4];   (* all vertices with fewer than four legs *)
FeynmanRules[L, Legs -> {4}]; (* all vertices with exactly four legs *)

In the output, Ext labels external fields and ExtMom their associated momenta.

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Notes

• FeynmanRules works on both renormalizable Lagrangians and higher-dimensional EFT Lagrangians.
• For theories defined in the symmetric phase, it is usually preferable to first apply spontaneous symmetry breaking and pass the broken-phase Lagrangian to FeynmanRules.
• The result is returned in Matchete’s internal tensor notation; NiceForm provides a readable printed form.
• A guide covering the full Feynman-rules and UFO workflow is available in the documentation.