论文标题
Feynman积分的部分微分方程的专业
Specializations of partial differential equations for Feynman integrals
论文作者
论文摘要
从梅林 - 巴恩斯（Mellin-Barnes）的积分表示从feynman积分的积分表示，具体取决于运动变量$ z_i $的集合，我们得出了一个部分微分方程的系统W.R.T.在我们的算法中，传播器的功能可以视为任意参数。我们的算法也可以用于将多个高几幅总和减少为较低维度的总和，在连续变量的奇异轨迹中找到特殊的值和降低高几幅函数的方程，或者找到具有传播器的任意功率的主积分的偏微分方程的系统。作为例证，我们在一个变量中为单环的两点Feynman图提供了一个第四阶的微分方程，该变量具有两个不同的质量和任意的传播器。
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the differentiable constraints $z_i=y_i(x_j)$. In our algorithm, the powers of propagators can be considered as arbitrary parameters. Our algorithm can also be used for the reduction of multiple hypergeometric sums to sums of lower dimension, finding special values and reduction equations of hypergeometric functions in a singular locus of continuous variables, or finding systems of partial differential equations for master integrals with arbitrary powers of propagators. As an illustration, we produce a differential equation of fourth order in one variable for the one-loop two-point Feynman diagram with two different masses and arbitrary propagator powers.
