GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions

Ulf Gran

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GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions

Ulf Gran

High Energy Physics - Theory · Submitted 10 May 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions.

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arXiv IDhep-th/0105086 (version 2)

Pith IDYVZAA5EC, Pith's permanent record of this paper and its review

CitationUlf Gran. "GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions." arXiv:hep-th/0105086 (2001). https://pith.science/paper/YVZAA5EC

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,188 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.20 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.34.

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We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions.	contribution 1.00	0.96	0.59	asserted 1.00
s1	As an application we can compute Fierz transformations.	contribution 0.67	0.87	0.17	asserted 0.53

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.81.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

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References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Algebraic structures on parallel M2-branes
hep-th 2007-09 conditional novelty 7.0 of 10

Supersymmetry closure on parallel M2-branes forces a specific non-Lie algebraic structure, with two sets of objects and three products obeying Jacobi identities.
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The authors derive the complete four-point tree-level effective action of type II superstrings to all orders in alpha prime, and show it equals the tensor product of two copies of the ten-dimensional super Yang-Mills action.
Supersymmetric AdS(4) compactifications of IIA supergravity
hep-th 2004-12 conditional novelty 6.0 of 10

N=1 supersymmetric AdS4 compactifications of massive IIA supergravity require a half-flat internal six-manifold with torsion in two specific classes, and all form fluxes are fixed by the internal geometry.
FormTracer - A Mathematica Tracing Package Using FORM
hep-ph 2016-10 conditional novelty 5.0 of 10

FormTracer wraps FORM in a Mathematica interface, adds a decomposition step that removes duplicate sub-traces across tensor spaces, and handles an arbitrary number of Lie groups plus the fifth gamma matrix in d dimensions.

Show 2 more citing papers

Introducing Cadabra: a symbolic computer algebra system for field theory problems
hep-th 2007-01 conditional novelty 5.0 of 10

Cadabra is introduced as a field-theory-specific computer algebra system whose TeX-like input and tensor, gamma-matrix and Fierz routines are demonstrated on concrete gravity and QFT calculations.
Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
hep-ph 2008-12 accept novelty 3.0 of 10

The paper compiles and explains a unified two-component spinor formalism with a complete set of fermion Feynman rules for the Standard Model, supersymmetry, and general quantum field theory.

How the literature uses it

31 arXiv papers cite this in 43 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Uses its method or tool 28 papers

Solving term by term with the help of the GAMMA package [ref] we obtain

Type I Supergravity Effective Action from Pure Spinor Formalism · One graviton/dilaton and two photons · 1.00
Therefore we can write [equation] After replacing [ref], [ref] in [ref] one obtains [equation] Next we use the $SO(9)$ Fierz identities [equation] which can be found by using the Mathematica package GAMMA [ref] , to obtain [equation] which implies [equation] where the constants $a$, $b$ will be determined from supersymmetry.

Pure spinors and $D=11$ supergravity · Light-cone gauge equations of motion · 0.95
We prove that our formulas give cocycles using Gamma [ref] .

Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra · Computer calculations · 1.00

Compares with it 1 paper

Our approach is substantially different from earlier packages, such as [ref] , in various ways: the approach we use is based on defining basic objects, such as spinors, gamma matrices and tensors.

"GammaMaP" - A Mathematica Package for Clifford Algebras, Gamma Matrices and Spinors · Introduction · 0.98

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