标题： 通过正交基和闭合公式进行费曼积分约简的交集理论 显示英文标题

标题： Feynman Integral Reductions by Intersection Theory with Orthogonal Bases and Closed Formulae

摘要： 我们提出一种选择正交基的方法，这些基属于二次扭曲周期积分的微分$n$-形式，并且相对于交数内积。 为了计算这些内积，我们另外提出一个关于交数的新封闭公式，超越$\mathrm{d} \log$形式。 这些发现使我们能够系统地在这一类扭曲周期积分之间构造正交规范基。 在费曼积分的背景下，这代表了一环图的所有图。 显示英文摘要

摘要： We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally propose a new closed formula for intersection numbers beyond $\mathrm{d} \log$ forms. These findings allow us to systematically construct orthonormal bases between twisted period integrals of this type. In the context of Feynman integrals, this represents all diagrams at one-loop.