PMA Publisher: Published from the Principia Machina source

2026-10-15T19:34:03Z

Published from the Principia Machina source

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	'''FeynCalc: Feynman Rules and Amplitudes from a Lagrangian'''		'''FeynCalc: Feynman Rules and Amplitudes from a Lagrangian'''
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	* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALC10\|FEYNCALC10]]''' – Shtabovenko V., Mertig R., Orellana F. (2025). FeynCalc 10: Do multiloop integrals dream of computer codes? Comput. Phys. Commun. 306, 109357. [https://doi.org/10.1016/j.cpc.2024.109357 doi:10.1016/j.cpc.2024.109357].		* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALC10\|FEYNCALC10]]''' – Shtabovenko V., Mertig R., Orellana F. (2025). FeynCalc 10: Do multiloop integrals dream of computer codes? Comput. Phys. Commun. 306, 109357. [https://doi.org/10.1016/j.cpc.2024.109357 doi:10.1016/j.cpc.2024.109357].
	* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALCREPO\|FEYNCALCREPO]]''' – FeynCalc developers. FeynCalc/feyncalc. [https://github.com/FeynCalc/feyncalc github.com/FeynCalc/feyncalc].		* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALCREPO\|FEYNCALCREPO]]''' – FeynCalc developers. FeynCalc/feyncalc. [https://github.com/FeynCalc/feyncalc github.com/FeynCalc/feyncalc].

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2026-10-06T03:41:02Z

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DeltaS Zero: Physics tool added 2026-10-06: FeynCalc; scores by the research pass, with references (tpm_toolkit 0.1.0)

2026-10-06T03:40:47Z

Physics tool added 2026-10-06: FeynCalc; scores by the research pass, with references (tpm_toolkit 0.1.0)

New page

'''FeynCalc: Feynman Rules and Amplitudes from a Lagrangian'''
[[Category:Principia Machina]] [[Category:Tools]]

''Added to the survey on 2026-10-06 by the [[The Principia Machina/Research Toolkit|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 Principia Machina/Tools#The additions of 2026-10-06|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 <math>k_\mu \mathcal{M}^\mu = 0</math>, the quantum shadow of a Noether symmetry, can be checked directly.

== Integration Pipeline ==
# '''Enter the Lagrangian''' and derive its vertices.
# '''Compute''' tree-level and one-loop amplitudes.
# '''Check''' the Ward identities that the action's gauge symmetry implies.
# '''Hand off''' to [[The Principia Machina/Tools/FORM|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 [[The Principia Machina/Agent/Tools|Agent/Tools]] and [[The Principia Machina/Tools/Operator's guide|the operator's guide]].

== References ==
* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALC10|FEYNCALC10]]''' – Shtabovenko V., Mertig R., Orellana F. (2025). FeynCalc 10: Do multiloop integrals dream of computer codes? Comput. Phys. Commun. 306, 109357. [https://doi.org/10.1016/j.cpc.2024.109357 doi:10.1016/j.cpc.2024.109357].
* '''[[The Principia Machina/Research Toolkit/Bibliography#FEYNCALCREPO|FEYNCALCREPO]]''' – FeynCalc developers. FeynCalc/feyncalc. [https://github.com/FeynCalc/feyncalc github.com/FeynCalc/feyncalc].

The Principia Machina/Tools/FeynCalc - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: Physics tool added 2026-10-06: FeynCalc; scores by the research pass, with references (tpm_toolkit 0.1.0)