6正则图和Feynman周期的保度三角维变换

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-10-14 DOI:10.4171/aihpd/172
S. Jeffries, K. Yeats
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引用次数: 2

摘要

我们研究了$\Delta$-Y变换的一个度保持变体,它将三角形替换为一个新的6价顶点,该顶点与三角形中的顶点具有双边。这个操作与理解6维的标量费曼积分有关。研究了该运算下等价类及其逆的结构,特别注意了等价类是有限的、包含简单6正则图和包含双3正则图的情况。其中最后一个,特别地,与费曼积分计算有关,我们做了一些观察,将这些类的结构与费曼周期联系起来。进一步研究了这些等价类中的极小图的性质。
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A degree preserving delta wye transformation with applications to 6-regular graphs and Feynman periods
We investigate a degree preserving variant of the $\Delta$-Y transformation which replaces a triangle with a new 6-valent vertex which has double edges to the vertices that had been in the triangle. This operation is relevant for understanding scalar Feynman integrals in 6 dimensions. We study the structure of equivalence classes under this operation and its inverse, with particular attention to when the equivalence classes are finite, when they contain simple 6-regular graphs, and when they contain doubled 3-regular graphs. The last of these, in particular, is relevant for the Feynman integral calculations and we make some observations linking the structure of these classes to the Feynman periods. Furthermore, we investigate properties of minimal graphs in these equivalence classes.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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