Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

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Manuscript Title: Feynman graph generation and calculations in the Hopf algebra of
Feynman graphs | ||

Authors: Michael Borinsky | ||

Program title: feyngen, feyncop | ||

Catalogue identifier: AEUB_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 185(2014)3317 | ||

Programming language: Python. | ||

Computer: PC. | ||

Operating system: Unix, GNU/Linux. | ||

RAM: 64m bytes | ||

Keywords: Quantum Field Theory, Feynman graphs, Feynman diagrams, Hopf algebra, Renormalization, BPHZ. | ||

PACS: 11.10.Gh, 11.15.Bt. | ||

Classification: 4.4. | ||

External routines: nauty [1], geng, multig (part of the nauty package) | ||

Nature of problem:Performing explicit calculations in quantum field theory Feynman graphs are indispensable. Infinities arising in the perturbative calculations make renormalization necessary. On a combinatorial level renormalization can be encoded using a Hopf algebra [2] whose coproduct incorporates the BPHZ procedure. Upcoming techniques initiated an interest in relatively large loop order Feynman diagrams which are not accessible by traditional tools. | ||

Solution method:Both programs use the established
package to
ensure high performance graph generation at high loop orders.nauty is capable of generating φfeyngen^{k}-theory,
QED
and Yang-Mills Feynman graphs and of filtering these graphs for the properties
of connectedness, one-particle-irreducibleness, 2-vertex-connectivity and
tadpole-freeness. It can handle graphs with fixed external legs as well as those
without fixed external legs. uses basic graph theoretical algorithms to compute the
coproduct
of graphs encoding their Hopf algebra structure.feyncop | ||

Running time:All 130516 1PI, φ^{4}, 8-loop diagrams
with four external legs can be generated, together with their symmetry factor,
by feyngen within eight hours and all 342430 1PI, QED, vertex
residue type, 6-loop diagrams can be generated in three days both on a standard
end-user PC. feyncop can calculate the coproduct of all 2346 1PI,
φ^{4}, 8-loop diagrams with four external legs within ten minutes. | ||

References: | ||

[1] | McKay, B.D., Practical Graph Isomorphism, Congressus Numerantium, 30
(1981) 45-87 | |

[2] | Connes and D. Kreimer, Renormalization in quantum eld theory and the
RiemannHilbert problem I. The Hopf algebra structure of graphs and the main
theorem, Commun. Math. Phys. 210 (2000) 249273. Letters in Mathematical
Physics 103 (9) (2013) 9331007 |

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