论文标题
双（椭圆）Feynman积分的逐环差分方程
Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
论文作者
论文摘要
我们提出了一种使用最近开发的双重形式形式主义计算Feynman积分的微分方程的逐环方法。我们为多环双重形式的逐环振动提供明确的处方。然后，我们在一个简单但非平凡的例子上测试形式主义：两环三质椭圆形的积分家族。我们以相对简单的代数步骤序列获得了正确函数空间内的Epsilon形式微分方程。特别是，这些步骤都不依赖于$ q $系列的分析。然后，我们讨论了通过双重基础所满足的有趣属性，以及它与Feynman Integrands的已知Epsilon形式基础的简单关系。还讨论了三循环四质量日出积分的基础K3几何。最后，我们推测如何在三环上构造“良好”环。
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an epsilon-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of $q$-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known epsilon-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a "good" loop-by-loop basis at three-loop.
