From multileg loops to trees (by-passing Feynman's Tree Theorem)

Geometrical approach to the evaluation of multileg Feynman diagrams

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a brief review of the results presented in hep-th/9709216).

利用量子最小化算法处理费曼积分

Tackling Feynman integrals with quantum minimization algorithms

针对多圈多腿费曼积分计算效率下降的问题，本文基于因果圈-树对偶性构建哈密顿量，并用变分量子本征求解器最小化散射振幅被积函数，展示量子计算带来加速与数值稳定性的潜力。

几何因果性：将费曼积分转化为量子算法

Geometrical causality: casting Feynman integrals into quantum algorithms

本文利用圈-树对偶性的几何因果选择规则构造哈密顿量，将费曼积分计算转化为最小化问题，并部署于量子计算机以寻求加速，旨在克服多圈多腿振幅计算中的资源瓶颈。

From loops to trees by-passing Feynman's theorem

We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be applied to generic one-loop quantities in any relativistic, local and unitary field theories. %It is suitable for applications to the analytica…