Parallel Computer Algebra and Feynman Integrals

2012 ◽  
pp. 13-16
Author(s):  
P. A. Baikov ◽  
K. G. Chetyrkin ◽  
J. H. Kühn ◽  
P. Marquard ◽  
M. Steinhauser ◽  
...  
Keyword(s):  
Computer Algebra ◽  
Parallel Computer ◽  
Feynman Integrals

Parallel computer algebra software as a Web component

1998 ◽  
Vol 10 (11-13) ◽  
pp. 1179-1188 ◽  
Author(s):  
Andreas Weber ◽  
Wolfgang Küchlin ◽  
Bernhard Eggers
Keyword(s):  
Computer Algebra ◽  
Parallel Computer ◽  
Computer Algebra Software ◽  
Web Component

scholarly journals DisCAS: A Distributed-Parallel Computer Algebra System

2004 ◽  
pp. 295-302
Author(s):  
Yongwei Wu ◽  
Guangwen Yang ◽  
Weimin Zheng ◽  
Dongdai Lin
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Parallel Computer

Parallel computer algebra on Poisson series

1996 ◽  
Vol 4 (4) ◽  
pp. 219-243 ◽  
Author(s):  
A. Fekken ◽  
D. Hilhorst ◽  
E.J.H. Kerckhoffs ◽  
P.R. Water
Keyword(s):  
Computer Algebra ◽  
Parallel Computer ◽  
Poisson Series

scholarly journals Application of a computer algebra systems to the calculation of the \(\pi\pi\)-scattering amplitude

2020 ◽  
Vol 28 (3) ◽  
pp. 216-229
Author(s):  
Yuriy L. Kalinovsky ◽  
Alexandra V. Friesen ◽  
Elizaveta D. Rogozhina ◽  
Lyubov’ I. Golyatkina
Keyword(s):  
Cross Section ◽  
Computer Algebra ◽  
Scattering Amplitude ◽  
Computer Algebra Systems ◽  
Zero Temperature ◽  
Feynman Integrals ◽  
Pion Scattering ◽  
Loop Approximation ◽  
Scattering Lengths ◽  
The One

The aim of this work is to develop a set of programs for calculation the scattering amplitudes of the elementary particles, as well as automating the calculation of amplitudes using the appropriate computer algebra systems (Mathematica, Form, Cadabra). The paper considers the process of pion-pion scattering in the framework of the effective Nambu-Iona-Lasinio model with two quark flavours. The Package-X for Mathematica is used to calculate the scattering amplitude (starting with the calculation of Feynman diagrams and ending with the calculation of Feynman integrals in the one-loop approximation). The loop integrals are calculated in general kinematics in Package-X using the Feynman parametrization technique. A simple check of the program is made: for the case with zero temperature, the scattering lengths \(a_0 = 0.147\) and \(a_2 = -0.0475\) are calculated and the total cross section is constructed. The results are compared with other models as well as with experimental data.

scholarly journals Distributed Maple: parallel computer algebra in networked environments

2003 ◽  
Vol 35 (3) ◽  
pp. 305-347 ◽  
Author(s):  
Wolfgang Schreiner ◽  
Christian Mittermaier ◽  
Karoly Bosa
Keyword(s):  
Computer Algebra ◽  
Parallel Computer

scholarly journals Computer algebra tools for Feynman integrals and related multi-sums

2018 ◽  
Author(s):  
Carsten Schneider ◽  
Johannes Blümlein
Keyword(s):  
Computer Algebra ◽  
Feynman Integrals

scholarly journals IBP reduction coefficients made simple

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Janko Boehm ◽  
Marcel Wittmann ◽  
Zihao Wu ◽  
Yingxuan Xu ◽  
Yang Zhang
Keyword(s):  
Computer Algebra ◽  
Efficient Method ◽  
Computer Algebra System ◽  
Size Reduction ◽  
Partial Fraction ◽  
Spacetime Dimension ◽  
Integral Basis ◽  
Feynman Integrals ◽  
Analytic Integration ◽  
Fraction Algorithm

Abstract We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas’ multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, we observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension D. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as ∼ 100. We observe that our algorithm also works well for settings without a UT basis.

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