Intersection theory, relative cohomology and the Feynman parametrization

2024/11/07 by Mingming Lu, Ziwen Wang, Lu, Mingming +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2411.05226

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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