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<p>We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction can then be achieved by computing intersection numbers. We apply our method in several examples to demonstrate its correctness, and discuss the subtleties in certain degenerate limits.</p>

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Intersection theory, relative cohomology and the Feynman parametrization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月20日

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  • Mingming Lu,
  • Ziwen Wang,
  • Li Lin Yang

摘要

We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction can then be achieved by computing intersection numbers. We apply our method in several examples to demonstrate its correctness, and discuss the subtleties in certain degenerate limits.