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FeynCalc 9.3: New features and improvements
Vladyslav Shtabovenko, Rolf Mertig, Frederik Orellana
TL;DR
Symbolic QFT calculations require coordination among multiple tools and careful treatment of algebraic and dimensional subtleties. FeynCalc 9.3 presents a stable Mathematica package with improved interoperability and expanded support for Majorana amplitudes and Dirac-matrix calculations. It also documents usage problems and workarounds, while noting that some symmetry-restoration and γ5 responsibilities remain with the user.
Problem
HEP calculations often require multiple tools, and users must handle dimensional-regularization and syntax issues that can produce incorrect results.
Method
The paper presents FeynCalc 9.3’s package features, interoperability mechanisms, dimensional-regularization procedures, and practical usage guidance.
Results
FeynCalc 9.3 supports loading with other Mathematica packages without shadowing issues when those packages do not conflict among themselves, and bypasses earlier limitations for Majorana traces.
Takeaways & Limitations
FeynCalc’s flexible, user-controlled workflow and community support make it a handy tool for professional and educational HEP use.
Takeaways & Limitations
γ5 calculations still require users to check relevant symmetries and restore violations with finite counterterms when necessary, especially beyond 1-loop.
Abstract
from arXiv · showhide
We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and $γ$-matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds.
1. Introduction
FeynCalc 9.3 is presented as a flexible Mathematica package for symbolic QFT calculations, addressing the difficulty of coordinating many specialized HEP tools. The paper introduces the release and discusses both its extensibility and performance trade-offs.
- Motivation: Feynman-diagram calculations often require multiple specialized codes, whose efficient, correct, and consistent interfacing is difficult.Different tools may automate different parts of a calculation, from deriving Feynman rules to obtaining observable predictions.
- FeynCalc’s role: FeynCalc is an open-source Mathematica package for manipulating Feynman amplitudes while preserving control over individual calculational steps.It can operate standalone or integrate into custom computational setups and is used across Standard Model, Beyond Standard Model, and Effective Field Theory calculations.
- FeynCalc’s role: Semi-automatic packages provide toolboxes for symbolic QFT operations such as index contractions, matrix simplification, loop-integral manipulation, and polarization sums.FeynCalc lets users perform these operations in an order guided by their own calculation, resembling pen-and-paper work.
- Design trade-offs: User-controlled flexibility makes FeynCalc suitable for calculations that automatic frameworks may not have anticipated or may not perform in a desired order.Automatic frameworks can be fast and easy to use, but their algorithms handle technical details under the hood and constrain calculation paths.
- Design trade-offs: FeynCalc’s Mathematica-based flexibility has lower performance than packages using faster symbolic systems such as FORM, especially for very large expressions.The limitation becomes more pressing as the numbers of diagrams, loops, legs, and expression terms increase.
2. Installation
The installation guidance covers automatic, manual, and development-version setups for FeynCalc 9.3, along with add-on loading and output customization. It also identifies compatibility boundaries for older Mathematica and Jupyter environments.
- Automatic installation: The automatic installer downloads the stable package snapshot and configures FeynArts to work with FeynCalc out of the box.Stable-branch bug fixes continue until the next official release, so periodic reinstallation can obtain a newer snapshot.
- Compatibility: Mathematica 8 and 9 may require offline or manual installation because of limitations accessing URLs through HTTPS.The project wiki provides instructions and workarounds for these older Mathematica versions.
- Add-ons: FeynCalc 9.3 reorganizes FeynArts and TARCER loading as add-ons, while retaining the old syntax for compatibility.The $LoadAddOns option accepts a list of strings, allowing multiple add-ons to be loaded together.
- Related packages: FeynRules can derive FeynArts models from a Lagrangian, while the FeynHelpers add-on interfaces with Package-X for analytic 1-loop integrals.These packages extend FeynCalc’s surrounding workflow for model implementation and loop-integral evaluation.
- Manual installation and configuration: Manual installation copies the FeynCalc directory into Mathematica’s Applications directory and renames DocOutput to Documentation for documentation support.The FCConfig.m file can contain initialization code, and dedicated commands switch TraditionalForm output on or off for new cells.
- Development version: The development version is maintained on the master branch and is merged into hotfix-stable when sufficiently stable for productive use.Users can install it with InstallFeynCalc[InstallFeynCalcDevelopmentVersion -> True], and feedback is encouraged through the mailing list or GitHub Issues.
3. New features in FEYNCALC 9.3
FeynCalc 9.3 improves interoperability, ultraviolet-divergence analysis, Majorana-spinor calculations, and manipulations involving explicit Dirac indices. It also introduces workarounds for package-name conflicts and previously difficult spinor-chain operations.
- Loading FEYNCALC together with other packages: FeynCalc 9.3 temporarily renames conflicting symbols, allowing the package to coexist with other Mathematica packages without shadowing interference.Renaming is session-specific and requires all evaluated code to use the modified symbols.
- Loading FEYNCALC together with other packages: The new loading mechanism imports package code as strings, enabling replacement of almost arbitrary FeynCalc symbol names through $RenameFeynCalcObjects.A minimal loader evaluates first, then performs name replacement before executing the remaining code.
- UV divergent parts of Passarino–Veltman functions: PaVeUVPart extracts ultraviolet-divergent parts of Passarino–Veltman functions without relying on Package-X and supports an arbitrary number of external legs.The functionality is useful for minimal-subtraction renormalization constants and checking ultraviolet-pole cancellation.
- UV divergent parts of Passarino–Veltman functions: PaVeUVPart handles only ultraviolet singularities, so a zero result does not establish infrared finiteness of the underlying Passarino–Veltman function.For example, C0 is always ultraviolet finite but can contain infrared poles depending on its kinematic invariants.
- Majorana spinors: Majorana-amplitude support adds automatic spinor-chain reordering, chain transposition, and charge-conjugation transposition for constructing traces and manipulating Dirac-matrix strings.FermionSpinSum can reorder closed chains, while SpinorChainTranspose and FCChargeConjugateTransposed provide explicit operations.
- Dirac matrices and spinors with explicit indices: Explicit Dirac-index support uses DiracIndex, DiracIndexDelta, and DiracChain, while FCFADiracChainJoin can determine relative signs for suitable four-fermion amplitudes.These additions address ambiguities that arise when more than two Dirac indices remain uncontracted.
4. Efficient usage of FEYNCALC in loop calculations
This section explains practical choices and pitfalls in FEYNCALC loop calculations, covering tensor-reduction speed, γ5 schemes, dimensional handling, and input validation.
- Faster 1-loop tensor reduction: Partial reduction into Passarino–Veltman coefficient functions keeps prefactors tensorial and results compact for symbolic and numerical evaluation.Unlike scalar-function reduction, coefficient-function results avoid huge polynomials of kinematic invariants.
- Faster 1-loop tensor reduction: Setting TID's UsePaVeBasis option to True enables a very fast partial tensor reduction similar to OneLoop.This addresses complaints that full TID reduction is slow, especially for generic kinematics.
- Treatment of γ5 in dimensional regularization: γ5 calculations require choosing among schemes because no universally accepted prescription automatically handles every model and loop order.Symmetry checks may still require restoring violated Ward identities or Bose symmetry with finite counterterms.
- Taking the correct limit D →4: Dimensional-regularization workflows require promoting or lowering quantities between four and D dimensions and expanding results around D = 4 in ε.FEYNCALC provides functions for these operations, but users must apply them correctly.
- Syntax checks: FCCheckSyntax searches inputs for common errors, helping beginners while avoiding an expensive checker that cannot detect every inconsistency.The package may otherwise accept incorrect expressions, such as using Times instead of Dot for Dirac or color matrix strings.
5. Summary
The paper presents FEYNCALC 9.3 as a stable QFT-symbolic-calculation release with broad new capabilities and guidance for everyday use. It also identifies experimental features and outlines future work toward faster, richer EFT and multiloop support.
- Summary: FEYNCALC 9.3 adds UV-divergence extraction for Passarino–Veltman functions, Majorana-spinor support, explicit Dirac indices, and improved package interoperability.It also automatically determines relative signs for four-fermion vertices generated with FEYNARTS.
- Summary: Most version 9.2–9.3 code changes concerned experimental Cartesian tensors, Pauli matrices, and nonstandard loop integrals for nonrelativistic calculations.Their symbols and routines were not yet finalized, so the paper only briefly documents them.
- Summary: FEYNCALC's flexible calculation organization, worked examples, and friendly community support its use for professional and educational HEP phenomenology.The authors characterize it as a handy tool within a HEP phenomenologist's software toolkit.
- Summary: Future plans emphasize faster, more feature-rich support for EFTs and multiloop calculations, including QGRAF integration, topology identification, and improved FORM interoperability.The FEYNONIUM project is intended to address EFTs, while additional multiloop routines are planned.
Appendix A. Experimental support for new propagators and tensor types
The appendix previews experimental support for Cartesian tensors, Pauli algebra, and loop integrals with nonstandard propagators. It demonstrates eikonal-integral manipulation while emphasizing that these capabilities remain under development.
- Experimental propagators and tensor types: SFAD lets users directly represent integrals with eikonal propagators and simplify them through operations such as partial fractioning.The paper presents this as an example beyond the reach of older FEYNCALC versions.
- Experimental propagators and tensor types: FEYNCALC 9.3 can manipulate the demonstrated eikonal integral into a partial-fractioned expression.The displayed output contains three terms with quadratic and eikonal denominator factors.
- Experimental propagators and tensor types: CFAD provides a Cartesian SFAD counterpart, while TID and FCMultiLoopTID support tensor reductions for ordinary and eikonal integrals respectively.Eikonal integrals may not reduce to scalar integrals with unit numerators.
- Experimental propagators and tensor types: Treatment of these nonstandard tensor integrals remains work in progress, with further improvements planned for subsequent versions.The appendix therefore presents the capabilities as experimental rather than finalized.