Computations and generation of elements on the Hopf algebra of Feynman graphs

16th International workshop on Advanced Computing and Analysis Techniques in physics research

物理学;计算机科学

Borinsky, Michael^1

Humboldt University Berlin, Departments of Physics and Mathematics, Unter den Linden 6, Berlin

10099, Germany^1

关键词: Co-products;    Combinatorics;    Field theory;    Hopf algebras;    K-Theory;    Loop order;    Zero-dimensional;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/608/1/012065/pdf
DOI  :  10.1088/1742-6596/608/1/012065

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Two programs, feyngen and feyncop, were developed. feyngen is designed to generate high loop order Feynman graphs for Yang-Mills, QED and φktheories. feyncop can compute the coproduct of these graphs on the underlying Hopf algebra of Feynman graphs. The programs can be validated by exploiting zero dimensional field theory combinatorics and identities on the Hopf algebra which follow from the renormalizability of the theories. A benchmark for both programs was made.