论文标题
高几何功能和Feynman图
Hypergeometric Functions and Feynman Diagrams
论文作者
论文摘要
讨论了Feynman图与超几何功能之间的关系。特别关注现有的技术，用于构建$ε$ -Expansion。例如，我们对Appell功能的Epsilon-Expansion的构建$ f_3 $的构建围绕参数的理性值进行了详细讨论。作为副产品，我们发现，尺寸为$ d =3-2ε$的单环无质量五边形图在多个小聚集体方面无法表达。另一个有趣的示例是涉及由三个变量的超几何函数生成的差分运算符的Puiseux型解。简要讨论了$ f_n $超几何功能的自动属性。
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $ε$-expansion. As an example, we present a detailed discussion of the construction of the epsilon-expansion of the Appell function $F_3$ around rational values of parameters via an iterative solution of differential equations. As a by-product, we have found that the one-loop massless pentagon diagram in dimension $d=3-2ε$ is not expressible in terms of multiple polylogarithms. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric function of three variables. The holonomic properties of the $F_N$ hypergeometric functions are briefly discussed.
