从计算代数几何的观点看分部积分约简
Integration-by-parts reductions from the viewpoint of computational algebraic geometry
摘要：
分部积分约化在微扰QFT计算中起着核心作用。它们允许一组费曼积分有助于一个给定的可观察到的减少到一个小的基础积分，而且他们方便这些基础积分的计算。我们介绍了一种有效的新方法，产生的积分的部分减少。这种方法通过利用广义酉割简化了任务，并将寻找所需的全导数的问题转化为求解某些多项式（所谓的syzygy）方程的问题。
英文摘要：
Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate the computation of those basis integrals. We introduce an efficient new method for generating integration-by-parts reductions. This method simplifies the task by making use of generalized-unitarity cuts and turns the problem of finding the needed total derivatives into one of solving certain polynomial (so-called syzygy) equations.
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