The Principia Machina/Tools/FeynCalc

FeynCalc: Feynman Rules and Amplitudes from a Lagrangian

Added to the survey on 2026-10-06 by the Research Toolkit's research pass. The scores below are that pass's assessment from the evidence cited under References, on the survey's four axes and scale; they are not the original survey's (2026-09-26), and no rule of the Principia Machina reads them. See the additions on the front page.

Overview & Architectural Fit

FeynCalc is a Mathematica package for symbolic quantum field theory: Dirac and colour algebra, tensor reduction, Feynman rules derived from a Lagrangian and, since version 10, the handling of multi-loop integrals. It is the interactive companion of FORM.

Mathematical Evaluation for TPM

• Lagrangian / Action (4.5/10): Derives Feynman rules from a Lagrangian, the step from action to vertices (the function was not re-checked in this pass); no classical variation.
• Field / PDE (2/10): Not a field or PDE tool.
• Relativity (3/10): Lorentz algebra in d dimensions.
• Quantum / Data (7.5/10): Interactive amplitude algebra, now with multi-loop support; Ward identities such as $k_{\mu }{ℳ}^{\mu }=0$, the quantum shadow of a Noether symmetry, can be checked directly.

Integration Pipeline

1. Enter the Lagrangian and derive its vertices.
2. Compute tree-level and one-loop amplitudes.
3. Check the Ward identities that the action's gauge symmetry implies.
4. Hand off to FORM when the expressions grow too large.

Status, Licence and Limits

• Status: Active. Version 10.2.1, June 2026; 10.2 in December 2025. The README lists Mathematica 10 to 14; Mathematica 15 (16 June 2026) is outside that range, compatibility not confirmed.
• Licence: GPL-3.0 or later; Mathematica is commercial.
• Home: https://github.com/FeynCalc/feyncalc
• Limits: Needs Mathematica. Not the right tool for very large multi-loop jobs.

On the Principia Machina

A tool runs only where the sponsor installed and bound it, and what it returns is untrusted input, vetted before use; its numbers are never values of the site's calculator, TPC. An equation it derives is transcribed into the kernel's form grammar before anything checks it, and lands as a RESULT of regime L with EQUATION and ROLE. See Agent/Tools and the operator's guide.

References

• FEYNCALC10 – Shtabovenko V., Mertig R., Orellana F. (2025). FeynCalc 10: Do multiloop integrals dream of computer codes? Comput. Phys. Commun. 306, 109357. doi:10.1016/j.cpc.2024.109357.
• FEYNCALCREPO – FeynCalc developers. FeynCalc/feyncalc. github.com/FeynCalc/feyncalc.