New developments in FeynCalc 9.0

详细信息    查看全文

• 作者：Vladyslav Shtabovenko^a ; ^{v.shtabovenko@tum.de" class="auth_mail" title="E-mail the corresponding author} ; Rolf Mertig^b ; ^{rolfm@gluonvision.com" class="auth_mail" title="E-mail the corresponding author} ; Frederik Orellana^c
• 关键词：High energy physics ; Feynman diagrams ; Loop integrals ; Dimensional regularization ; Dirac algebra ; Color algebra ; Tensor reduction
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：207
• 期：Complete
• 页码：432-444
• 全文大小：612 K

文摘

In this note we report on the new version of FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory. The main features of version 9.0 are: improved tensor reduction and partial fractioning of loop integrals, new functions for using FeynCalc together with tools for reduction of scalar loop integrals using integration-by-parts (IBP) identities, better interface to FeynArts and support for SU(N)$SU\left(N\right)$ generators with explicit fundamental indices.

Program summary

Program title: FeynCalc

Catalogue identifier: AFBB_v1_0

Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBB_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: GNU Public Licence 3

No. of lines in distributed program, including test data, etc.: 734115

No. of bytes in distributed program, including test data, etc.: 6890074

Distribution format: tar.gz

Programming language: Wolfram Mathematica 8 and higher.

Computer: Any computer that can run Mathematica 8 and higher.

Operating system: Windows, Linux, OS X.

Classification: 4.4, 5, 11.1.

External routines: FeynArts [2] (Included)

Nature of problem: Symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory.

Solution method: Algebraic identities that are needed for evaluation of Feynman

Reasons for new version: Compatibility with Mathematica 10, improved performance and new features regarding manipulation of loop integrals.

Restrictions:   Slow performance for multi-particle processes (beyond 1→2$1\to 2$ and 2→2$2\to 2$) and processes that involve large (>$>$100) number of Feynman diagrams.

Additional comments: The original FeynCalc paper was published in Comput. Phys. Commun., 64 (1991) 345, but the code was not included in the Library at that time.

Reasons for the new version: Compatibility with Mathematica 10, improved performance and new features regarding manipulation of loop integrals.

Summary of revisions: Tensor reduction of 1-loop integrals is extended to arbitrary rank and multiplicity with proper handling of integrals with zero Gram determinants. Tensor reduction of multi-loop integrals is now also available (except for cases with zero Gram determinants). Partial fractioning algorithm of [1] is added to decompose loop integrals into terms with linearly independent propagators. Feynman diagrams generated by FeynArts can be directly converted into FeynCalc input for subsequent evaluation.

Running time: Depends on the complexity of the calculation. Seconds for few simple tree level and 1-loop Feynman diagrams; Minutes or more for complicated diagrams.

References:

[1]

F. Feng, $Apart: A Generalized Mathematica Apart Function, Comput. Phys. Commun., 183, 2158–2164, (2012), arXiv:1204.2314.

[2]

T. Hahn, Generating Feynman Diagrams and Amplitudes with FeynArts 3, Comput. Phys. Commun., 140, 418–431, (2001), arXiv:hep-ph/0012260.