标题： 不同时空维度的费曼积分之间的关系 显示英文标题

标题： Connection between Feynman integrals having different values of the space-time dimension

摘要： 一种系统算法用于获得关于时空维度$d$的维数正则化费曼积分的递推关系被提出。$d$和$d-2$维度积分之间的关系是通过一个微分算子给出的，对于每个费曼图都可以得到该算子的显式公式。我们展示了该方法如何应用于一环、二环和三环积分。相对于$d$的新递推关系与从分部积分方法导出的递推关系是互补的。我们发现，在所提出的广义递推关系框架中，费曼积分中不可约分子的问题可以自然地得到解决。 显示英文摘要

摘要： A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two- and three-loop integrals. The new recurrence relations w.r.t. $d$ are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations.