Recently, a nice work about the understanding of one-loop integrals has been given by Arkani-Hamed and Yuan [arXiv:1712.09991] using the language of the projective space associated to their Feynman parametrization. We find this language is also very suitable to deal with the reduction problem of one-loop integrals with general tensor structures as well as propagators having arbitrary higher powers. In this paper, we show how to combine Feynman parametrization and embedding formalism to give a universal treatment of reductions for general one-loop integrals, even including the degenerated cases, such as the vanishing Gram determinant. Results from this method can be written in a compact and symmetric form.

中文翻译：

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射影空间中单环积分约简的通用处理

最近，Arkani-Hamed 和 Yuan [arXiv:1712.09991] 使用与他们的 Feynman 参数化相关的射影空间语言，就理解单环积分做出了很好的工作。我们发现这种语言也非常适合处理具有一般张量结构的单环积分以及具有任意更高幂的传播器的约简问题。在本文中，我们展示了如何结合 Feynman 参数化和嵌入形式来对一般单环积分的归约进行通用处理，甚至包括退化的情况，例如消失的 Gram 行列式。这种方法的结果可以写成紧凑和对称的形式。