RGIsearch: A C++ program for the determination of renormalization group invariants

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• 作者：Rob Verheyen ^{RobVerheyen@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Renormalization ; Computer algebra ; Sparse linear systems
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：351-355
• 全文大小：379 K

文摘

RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the β$\beta$-functions of quantum field theories, RGIsearch searches for several types of invariants that require different methods. Additionally, it supports the computation of invariants up to two-loop level. A manual for the program is given, including the settings and set-up of the program, as well as a test case.

Program summary

Program title: RGIsearch

Catalogue identifier: AEZQ_v1_0

Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZQ_v1_0.html

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

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 129911

No. of bytes in distributed program, including test data, etc.: 8364946

Distribution format: tar.gz

Programming language: C++.

Computer: Desktop PC.

Operating system: Linux.

RAM: Ranging from several MB to several GB

Classification: 2.9, 4.8, 5.

Nature of problem: The determination of renormalization group invariants, which can be used as a probe for the high-energy behavior of theories in particle physics.

Solution method: Several types of invariants are considered based on the general shape of the renormalization group equations. The problem of computing these invariants is then reduced to creating and solving very large systems of linear equations or generalized eigenvalue problems. Using the specific sparsity structure of these systems, the systems can be solved.

Restrictions: Since the algorithms that solve the linear systems and generalized eigenvalue problems are very efficient, the main restriction is the amount of available RAM, where the systems are stored. The program supports polynomial renormalization group equations, which are typical particle physics, up to two-loop order.

Running time: Ranging from seconds to minutes